ACT Math - Trapezoids | Practice Hub

1

Given the following isosceles triangle:

In degrees, find the measure of the sum of $\angle x$ and $\angle$ in the figure above.

$120^\circ$

$30^\circ$

$60^\circ$

$180^\circ$

$240^\circ$

Explanation

All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.

Similarly, the two bottom angles are equal to each other as well.

Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:

2

Given the following isosceles triangle:

In degrees, find the measure of the sum of $\angle x$ and $\angle$ in the figure above.

$120^\circ$

$30^\circ$

$60^\circ$

$180^\circ$

$240^\circ$

Explanation

All quadrilaterals' interior angles sum to 360°. In isosceles trapezoids, the two top angles are equal to each other.

Similarly, the two bottom angles are equal to each other as well.

Therefore, to find the sum of the two bottom angles, we subtract the measures of the top two angles from 360:

3

A trapezoid has bases of length and and side lengths of and . What is the upper non-inclusive limit of the trapezoid's diagonal length?

Explanation

The upper limit of a trapezoid's diagonal length is determined by the lengths of the larger base and larger side because the larger base, larger side and longest diagonal form a triangle, meaning you can use a triangle's side length rule.

Specifically, the non-inclusive upper limit will be the sum of the larger base and larger side.

In this case, , meaning that the diagonal length can go up to but not including .

4

A trapezoid has bases of length and and side lengths of and . What is the upper non-inclusive limit of the trapezoid's diagonal length?

Explanation

The upper limit of a trapezoid's diagonal length is determined by the lengths of the larger base and larger side because the larger base, larger side and longest diagonal form a triangle, meaning you can use a triangle's side length rule.

Specifically, the non-inclusive upper limit will be the sum of the larger base and larger side.

In this case, , meaning that the diagonal length can go up to but not including .

5

Suppose the lengths of the bases of a trapezoid are 1 and 5 respectively. The altitude of the trapezoid is 4. What is the diagonal of the trapezoid?

$\sqrt{17}$

$\sqrt{39}$

Explanation

The altitude of the trapezoid splits the trapezoid into two right triangles and a rectangle. Choose one of those right triangles. The base length of that right triangle is necessary to solve for the diagonal.

Using the base lengths of the trapezoid, the length of the base of the right triangle can be solved. The length of the rectangle is 1 unit. The longer length of the trapezoid base is 5 units.

Since there are 2 right triangles bases that lie on the longer base of the trapezoid, we will assume that their base lengths are since their lengths are unknown. Combining the lengths of the right triangles and the rectangle, write the equation to solve for the length of the right triangle bases.

The length of each triangular base is 2.

The diagonal of the trapezoid connects from either bottom angle of the trapezoid to the far upper corner of the rectangle. This diagonal connects to form another right triangle, where the sum of the solved triangular base and the rectangle length is a leg, and the altitude of the trapezoid is another leg.

$\textup{Sum of a triangular base and the rectangle length= }2+1=3$

$\textup{Altitude of trapezoid= }4$

Use the Pythagorean Theorem to solve for the diagonal.

6

Suppose the lengths of the bases of a trapezoid are 1 and 5 respectively. The altitude of the trapezoid is 4. What is the diagonal of the trapezoid?

$\sqrt{17}$

$\sqrt{39}$

Explanation

The altitude of the trapezoid splits the trapezoid into two right triangles and a rectangle. Choose one of those right triangles. The base length of that right triangle is necessary to solve for the diagonal.

Using the base lengths of the trapezoid, the length of the base of the right triangle can be solved. The length of the rectangle is 1 unit. The longer length of the trapezoid base is 5 units.

Since there are 2 right triangles bases that lie on the longer base of the trapezoid, we will assume that their base lengths are since their lengths are unknown. Combining the lengths of the right triangles and the rectangle, write the equation to solve for the length of the right triangle bases.

The length of each triangular base is 2.

The diagonal of the trapezoid connects from either bottom angle of the trapezoid to the far upper corner of the rectangle. This diagonal connects to form another right triangle, where the sum of the solved triangular base and the rectangle length is a leg, and the altitude of the trapezoid is another leg.

$\textup{Sum of a triangular base and the rectangle length= }2+1=3$

$\textup{Altitude of trapezoid= }4$

Use the Pythagorean Theorem to solve for the diagonal.

7

Find the area of a trapezoid given bases of length 6 and 7 and height of 2.

$\frac{13}{2}$

Explanation

To solve, simply use the formula for the area of a trapezoid.

Substitute

into the area formula.

Thus,

$A=\frac{1}{2}(B1+B2)h=\frac{1}{2}(6+7)*2=6+7=13$

8

Find the area of a trapezoid given bases of length 6 and 7 and height of 2.

$\frac{13}{2}$

Explanation

To solve, simply use the formula for the area of a trapezoid.

Substitute

into the area formula.

Thus,

$A=\frac{1}{2}(B1+B2)h=\frac{1}{2}(6+7)*2=6+7=13$

9

Trap

What is the area of the trapezoid above if a = 2, b = 6, and h = 4?

16

32

8

64

24

Explanation

Area of a Trapezoid = ½(a+b)*h

= ½ (2+6) * 4

= ½ (8) * 4

= 4 * 4 = 16

10

Trap

What is the area of the trapezoid above if a = 2, b = 6, and h = 4?

16

32

8

64

24

Explanation

Area of a Trapezoid = ½(a+b)*h

= ½ (2+6) * 4

= ½ (8) * 4

= 4 * 4 = 16

Trapezoids

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation