Geometry

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ISEE Middle Level Quantitative Reasoning › Geometry

Questions 1 - 10
1

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:

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.

2

What is the perimeter of a square with area 196 square inches?

It cannot be determined from the information given.

Explanation

A square with area 196 square inches has sidelength inches, and therefore has perimeter inches

3

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, , we can solve for the area of both of our rectangles

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

4

Annie has a piece of wallpaper that is by . How much of a wall can be covered by this piece of wallpaper?

Explanation

This problem asks us to calculate the amount of space that the wallpaper will cover. The amount of space that something covers can be described as its area. In this case area is calculated by using the formula

5

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

Explanation

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

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

6

What is the area of the figure below?

12

Explanation

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

12.5

Using our area formula, , we can solve for the area of both of our rectangles

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

7

What is the length of a rectangular room with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

8

What is the area of the figure below?

6

Explanation

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

6.5

Using our area formula, , we can solve for the area of both of our rectangles

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

9

What is the area of the figure below?

6

Explanation

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

6.5

Using our area formula, , we can solve for the area of both of our rectangles

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

10

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

Explanation

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

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

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