Quadrilaterals

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ISEE Middle Level Quantitative Reasoning › Quadrilaterals

Questions 1 - 10

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

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

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

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 $\frac{49}{16} : 1 = 49:16$ .

Rectangle

Give the area of the above rectangle in square feet.

$216 \textrm{ ft}^{2}$

$532\textrm{ ft}^{2}$

$576 \textrm{ ft}^{2}$

$33 \textrm{ ft}^{2}$

$66 \textrm{ ft}^{2}$

Explanation

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

$8 \textrm{ yd} \times 3 \textrm{ ft/yd} = 24 \textrm{ ft}$

$3 \textrm{ yd} \times 3 \textrm{ ft/yd} = 9 \textrm{ ft}$

Use the area formula, substituting :

$A = 24 \times 9 = 216$ square feet

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

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

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

Angela has a garden that she wants to put a fence around. How much fencing will she need if her garden is by

Explanation

The fence is going around the garden, so this is a perimeter problem.

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

$56 ; \textrm{in}$

$28 ; \textrm{in}$

$112 ; \textrm{in}$

$64; \textrm{in}$

It cannot be determined from the information given.

Explanation

A square with area 196 square inches has sidelength $\sqrt{196} = 14$ inches, and therefore has perimeter $4 \cdot 14 = 56$ inches

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 $A=l \times w$