How to find the area of a parallelogram - Geometry

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Question

Find the area of the box in square inches:

Answer

The answer is . You can find the area of this box by multiplying the length by its width:

Foil

If you chose , you added the sides to get the perimeter.

Just remember, the width is 12 added to . Not 12 times the side of .

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Question

The perimeter of a square is . If the sides of the square are reduced by a factor of two, what is the area of the new square?

Answer

The perimeter of a square is geven by and the area of a square is given by $A=s^{2}$ .

Thus

so .

The original side is reduced by a factor of which results in a new side of . The area of the new square is geven by

$A=s^{2}=3^{2}=9; in^{2}$

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Question

If all angles are right angles in the figure below, what is the total area of the figure?

Answer

The answer is $164\ in^{2}$ .

To get the area, you would need to find the missing sides. Since the horizontal top is inches total, the bottom must be inches total. Thus you would subtract to get for the missing bottom horizontal side.

The vertical right side is inches total. Then you would subtract to get for the missing vertical side.

Then you would have to split the figure into 3 different boxes and find the area of each one. Then you would add the area of each box

$(32+60+72)=164\ in ^{2}$

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Question

Find the area of the parallelogram.

Note that the figure is not drawn to scale.

Answer

The area of a parallelogram can be found using the following equation:

In this problem, the height is 6 (not 8). Substitute the known variables and solve.

$A=14\times 6$

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Question

In the figure, the area of the parallelogram is . Find the length of the base.

Answer

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=(\text{base})(\text{height})$

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

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Question

What is the area of a parallelogram if the base is , and the height is ?

Answer

The formula for the area of a parallelogram is:

$A=base\cdot height$

So, we are given all of the information that we need to solve this problem. Substitute the provided values into the equation and simplify:

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Question

What is the area of a parallelogram if the base is and the height is ?

Answer

The formula for the area of a parallelogram is:

$A=base\cdot height$

Substitute in the provided values and simplify to calculate the correct answer:

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Question

Find the area of a parallelogram if the base is and the height is .

Answer

The formula for the area of a parallelogram is:

$A=base\cdot height$

Substitute the values provided in the question:

Use the FOIL method to simplify:

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Question

What is the area of a parallelogram if the base is $\sqrt2:cm$ and the height is $\sqrt3:cm$ ?

Answer

The formula for the area of a parallelogram is:

$A=base\cdot height$

Substitute the values provided in the problem and solve to calculate the correct answer:

$A= (\sqrt2:cm)(\sqrt3:cm) =\sqrt6:cm^2$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=8 \times 14$

$\text{Area of Rectangle}=112$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{8}{2}$

$\text{height}=4$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=10 \times 4$

$\text{Area of Parallelogram}=40$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=112-40$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=2 \times 6$

$\text{Area of Rectangle}=12$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{2}{2}$

$\text{height}=1$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=3 \times 1$

$\text{Area of Parallelogram}=3$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=12-3$

Solve.

$\text{Area of Shaded Region}=9$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=4 \times 12$

$\text{Area of Rectangle}=48$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{4}{2}$

$\text{height}=2$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=8 \times 2$

$\text{Area of Parallelogram}=16$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=48-16$

Solve.

$\text{Area of Shaded Region}=32$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=12 \times 20$

$\text{Area of Rectangle}=240$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{12}{2}$

$\text{height}=6$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=15 \times 6$

$\text{Area of Parallelogram}=\90$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=240-90$

Solve.

$\text{Area of Shaded Region}=150$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=16\times 22$

$\text{Area of Rectangle}=352$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{16}{2}$

$\text{height}=8$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=12 \times 8$

$\text{Area of Parallelogram}=96$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=352-96$

Solve.

$\text{Area of Shaded Region}=256$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=4 \times 8$

$\text{Area of Rectangle}=32$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{4}{2}$

$\text{height}=2$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=7\times 2$

$\text{Area of Parallelogram}=14$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=32-14$

Solve.

$\text{Area of Shaded Region}=18$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=3\times12$

$\text{Area of Rectangle}=36$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{3}{2}$

$\text{height}=1.5$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=5\times 1.5$

$\text{Area of Parallelogram}=7.5$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=36-7.5$

Solve.

$\text{Area of Shaded Region}=28.5$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=20\times 25$

$\text{Area of Rectangle}=500$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{20}{2}$

$\text{height}=10$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=18\times 10$

$\text{Area of Parallelogram}=180$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=500-180$

Solve.

$\text{Area of Shaded Region}=320$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=30\times 32$

$\text{Area of Rectangle}=960$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{30}{2}$

$\text{height}=15$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=26\times 15$

$\text{Area of Parallelogram}=390$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=960-390$

Solve.

$\text{Area of Shaded Region}=570$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=40\times 30$

$\text{Area of Rectangle}=1200$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{30}{2}$

$\text{height}=15$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=26\times 15$

$\text{Area of Parallelogram}=390$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=1200-390$

Solve.

$\text{Area of Shaded Region}=810$

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Question

If the height of the parallelogram is half of the length of the rectangle, then find the area of the shaded region in the figure.

Answer

In order to find the area of the shaded region, we must first find the areas of the rectangle and parallelogram.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

Substitute in the given length and height to find the area of the rectangle.

$\text{Area of Rectangle}=6\times 40$

$\text{Area of Rectangle}=240$

Next, find the area of the parallelogram.

Recall how to find the area of a parallelogram:

$\text{Area of Parallelogram}=\text{base}\times\text{height}$

We need to find the height of the parallelogram. From the question, we know the following relationship:

$\text{height}=\frac{\text{length}}{2}$

Substitute in the length of the rectangle to find the height of the parallelogram.

$\text{height}=\frac{6}{2}$

$\text{height}=3$

Now, substitute in the height and the given length of the base to find the area of the parallelogram.

$\text{Area of Parallelogram}=15 \times 3$

$\text{Area of Parallelogram}=45$

Now, we are ready to find the area of the shaded region by subtracting the area of the parallelogram from the area of the rectangle.

$\text{Area of Shaded Region}=\text{Area of Rectangle}-\text{Area of Parallelogram}$

$\text{Area of Shaded Region}=240-45$

Solve.

$\text{Area of Shaded Region}=195$

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