Plane Geometry

Help Questions

ISEE Middle Level Quantitative Reasoning › Plane 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

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

3

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

4

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

Cannot be determined from the information provided.

Explanation

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the arms are 1.5 feet, what is the perimeter of the base of your new bookshelf?

To find the perimeter of a bookshelf, we need to add up the lengths of the sides.

We know the two bases, we just need to add the lengths of the arms.

So, our answer is 8ft

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 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

7

Rectangle

Give the area of the above rectangle in square feet.

Explanation

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

Use the area formula, substituting :

square feet

8

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 , and its area is .

The perimeter of the first square is , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

9

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

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

Page 1 of 100
Return to subject