How to find the area of a rectangle - Geometry

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Question

What is the area of the rectangle in the diagram?

Answer

The area of a rectangle is found by multiplying the length by the width.

The length is 12 cm and the width is 7 cm.

$12\cdot 7=84$

Therefore the area is 84 cm2.

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Question

A rectangle has a perimeter of . The length is ten meters more than the width. What is the area of the rectangle?

Answer

Given a rectangle, the general equation for the perimeter is and area is where is the length and is the width.

Let = width and = length

So the equation to solve becomes so thus the width is and the length is .

Thus the area is $5\cdot 15= 75 ; m^{2}$

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Question

Which of the following information would not be sufficient to find the area of a rectangle?

Answer

The area of a rectangle can be calculated by multiplying the lengths of two adjacent sides. All of the choices given lists sufficient information, with one exception. We examine each of the choices.

The lengths of one pair of adjacent sides: This choice is false, as is directly stated above.

The perimeter and the length of one side: Using the perimeter formula, you can find the length of an adjacent side, making this choice false.

The lengths of one side and a diagonal: using the Pythagorean Theorem, you can find the length of an adjacent side, making this choice false.

The lengths of one pair of opposite sides: this gives you no way of knowing the lengths of the adjacent sides. This is the correct choice.

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Question

Find the area of the polygon.

Answer

Drawing a vertical line at the end of the side of length divides the shape into a rectangle and a right triangle.

The sum of the areas of the two shapes is the area of the polygon. Multiply the length of the rectangle by its width to find the area of the rectangle, and use the formula $A = \frac{1}{2}bh$ , where is the base and is the height of the triangle, to find the area of the triangle. Adding them together gives the answer.

$A_{total}=A_{rec}+A_{tri}$

$A_{total}=(820)+\frac{1}{2}(58)$

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Question

One side of a rectangle is 7 inches and another is 9 inches. What is the area of the rectangle in inches?

Answer

To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.

$9\cdot 7=63$

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Question

What is the area of a rectangle whose length and width is inches and inches, respectively?

Answer

The area of any rectangle with length, and width, is:

$A=l\times w$

$A=14\times 18$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=2 \times 20=40$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=12 \times 10= 120$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=8 \times 30= 240$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=100 \times 4= 400$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=65 \times 20= 1300$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=90 \times 40= 3600$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

$\text{Area}=18 \times 6= 108$

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Question

What is the area of a rectangle that has a length of $\frac{4}{5}$ and a width of $\frac{1}{2}$ ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying fractions, multiply the numerators together and multiply the denominators together. After multiplication is done, find common factors in the numerator and denominator to cancel out and completely simplify the fraction.

$\ \text{Area}=\frac{4}{5} \times \frac{1}{2}\ \ \text{Area}=\frac{4}{10}=\frac{2\cdot 2}{2\cdot 5}\ \\text{Area}= \frac{2}{5}$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying decimals together first move the decimal over so that the number is a whole integer.

$1.8\rightarrow 18, 2.5\rightarrow 25$

Now we multiple the integers together.

$1.8\cdot 2.5\rightarrow 18\cdot 25=450$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one time for each number for a total of two decimal places.

Therefore our answer becomes,

$450\rightarrow 4.50$

$\text{Area}=1.8 \times 2.5= 4.5$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying decimals together first move the decimal over so that the number is a whole integer.

$12.5\rightarrow 125$

Now we multiple the integers together.

$12.5\cdot 10\rightarrow 125\cdot 10=1250$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over one place.

Therefore our answer becomes,

$1250\rightarrow 125.0$

$\text{Area}=12.5 \times 10= 125$

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Question

What is the area of a rectangle that has a length of and a width of ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying decimals together first move the decimal over so that the number is a whole integer.

$0.75\rightarrow 75$

Now we multiple the integers together.

$0.75\cdot 85\rightarrow 75\cdot 85=6375$

From here, we need to move the decimal place back. In this particular problem we moved the decimal over a total of two decimal places.

Therefore our answer becomes,

$6375\rightarrow 63.75$

$\text{Area}=85 \times 0.75= 63.75$

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Question

What is the area of a rectangle that has a length of and a width of $\frac{1}{7}$ ?

Answer

Recall how to find the area of a rectangle:

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

Now, plug in the given length and width to find the area.

When multiplying fractions, multiply the numerators together and multiply the denominators together. After multiplication is done, find common factors in the numerator and denominator to cancel out and completely simplify the fraction. In this particular case the integer can be written as a fraction by putting it over one.

$\textup{Area}=\frac{63}{1}\times \frac{1}{7}$

$\text{Area}= \frac{1 \times 63 }{7\times 1}= \frac{63}{7}=\frac{7\cdot 9}{7}=9$

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Question

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Answer

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$

From this equation, we can solve for the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{24}{2}-5=7$

Simplify.

$\text{Width}=7$

Now, recall how to find the area of a rectangle:

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

Substitute in the information about the length and width to find the area for the rectangle in question.

$\text{Area}=5 \times 7$

Solve.

$\text{Area}=35$

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Question

If the perimeter of a rectangle is , and the length of the rectangle is , what is the area of the rectangle?

Answer

First, use the information given about the perimeter to find the width of the rectangle.

Recall how to find the perimeter of a rectangle:

$\text{Perimeter}=2(\text{length}+\text{width})$

From this equation, we can solve for the width.

$\text{length}+\text{width}=\frac{\text{Perimeter}}{2}$

$\text{width}=\frac{\text{Perimeter}}{2}-\text{length}$

Substitute in the information from the question to find the width of the rectangle.

$\text{Width}=\frac{18}{2}-6$

Simplify.

$\text{Width}=3$

Now, recall how to find the area of a rectangle:

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

Substitute in the information about the length and width to find the area for the rectangle in question.

$\text{Area}=6 \times 3$

Solve.

$\text{Area}=18$

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