How to find the area of a rectangle

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ISEE Middle Level Quantitative Reasoning › How to find the area of a rectangle

Questions 1 - 10

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

Explanation

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

To find the area of a rectangle, we must perform the following:

$A_{Rectangle}=l*w$

Where l and w are our length and width.

This means we need to multiply the given measurements. Be sure to use the right units!

And we have our answer. It must be centimeters squared, because we are dealing with area.

Find the area of a rectangle with a length of 14in and a width that is half the length.

$98\text{in}^2$

$42\text{in}^2$

$21\text{in}^2$

$7\text{in}^2$

$72\text{in}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 14in. We also know the width of the rectangle is half the length. Therefore, the width is 7in.

Knowing this, we will substitute into the formula. We get

$\text{area of rectangle} = 14\text{in} \cdot 7\text{in}$

$\text{area of rectangle} = 98\text{in}^2$

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

Find the area of a rectangle with a length of 12cm and a width that is a quarter of the length.

$36\text{cm}^2$

$48\text{cm}^2$

$16\text{cm}^2$

$25\text{cm}^2$

$30\text{cm}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 12cm. We also know the width of the rectangle is a quarter of the length. To find the width, we will divide 12 by 4. Therefore, the width the 3cm.

Knowing this, we will substitute into the formula. We get

$\text{area of rectangle} = 12\text{cm} \cdot 3\text{cm}$

$\text{area of rectangle} = 36\text{cm}^2$

What is the area of the figure below?

6.5

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

6.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=5\times 10$ $A=5\times 3$

To find our final answer, we need to add the areas together.

Find the area of a rectangle with a length of 16cm and a width that is a quarter of the length.

$64\text{cm}^2$

$128\text{cm}^2$

$31\text{cm}^2$

$32\text{cm}^2$

$62\text{cm}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 16cm. We also know the width of the rectangle is a quarter of the length. To find the width, we will divide 16 by 4. Therefore, the width the 4cm.

Knowing this, we will substitute into the formula. We get

$A = 16\text{cm} \cdot 4\text{cm}$

$A = 64\text{cm}^2$

Use the following image to answer the question:

Rectangle3

Find the area of the rectangle.

$54\text{in}^2$

$30\text{in}^2$

$15\text{in}^2$

$63\text{in}^2$

$36\text{in}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, let's look at the rectangle.

Rectangle3

We can see the length is 9 inches, and the width is 6 inches.

Knowing this, we can substitute into the formula. We get

$\text{area of rectangle} = 9\text{in} \cdot 6\text{in}$

$\text{area of rectangle} = 54\text{in}^2$

Find the area of a rectangle with a length of 24in and a width that is a third of the length.

$192\text{in}^2$

$72\text{in}^2$

$96\text{in}^2$

$156\text{in}^2$

$212\text{in}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$A = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the length of the rectangle is 24in. We also know the width is a third of the length. Therefore, the width is 8in.

Knowing this, we can substitute into the formula. We get

$A = 24\text{in} \cdot 8\text{in}$

$A = 196\text{in}^2$

Find the area of a rectangle with a width of 9cm and a length that is two times the width.

$162\text{cm}^2$

$128\text{cm}^2$

$18\text{cm}^2$

$24\text{cm}^2$

$32\text{cm}^2$

Explanation

To find the area of a rectangle, we will use the following formula:

$\text{area of rectangle} = l \cdot w$

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 9cm. We also know the length of the rectangle is two times the width. Therefore, the length is 18cm.

Knowing this, we will substitute into the formula. We get

$\text{area of rectangle} = 18\text{cm} \cdot 9\text{cm}$

$\text{area of rectangle} = 162\text{cm}^2$

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 3$ $A=6\times 3$

To find our final answer, we need to add the areas together.

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