Exercises: Area and perimeter of triangles - ACT Math

A

Recall / Warm-Up

1.

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

A.

13

B.

17

C.

7

D.

60

2.

A triangle has sides of length 7, 7, and 10. How is this triangle classified by its sides?

A.

Equilateral

B.

Isosceles

C.

Scalene

D.

Right

3.

What is the perimeter of a triangle with sides 9, 12, and 15?

B

Fluency Practice

1.

A right triangle has legs 6 cm and 8 cm. What is the area in square centimeters?

2.

A triangle has a base of 14 in and a perpendicular height of 9 in. What is its area?

A.

126 in²

B.

63 in²

C.

46 in²

D.

23 in²

3.

A right triangle has legs 5 cm and 12 cm. What is the perimeter in centimeters?

4.

What is the area of an equilateral triangle with side length 6?

A.

$9\sqrt{3}$

B.

$18\sqrt{3}$

C.

18

D.

9

5.

A triangle has vertices at $(1, 1)$ , $(5, 1)$ , and $(3, 5)$ . What is the area?

C

Varied Practice

D

Word Problems / Application

1.

A triangular garden has a base of 14 feet and a height of 9 feet. The owner wants to cover the entire garden with mulch.

How many square feet of mulch are needed to cover the garden?

2.

A sail on a boat is shaped like a right triangle with legs of 6 m and 8 m. The sailmaker needs to know the perimeter to add trim around the edges.

What is the perimeter of the sail?

A.

14 m

B.

24 m

C.

48 m

D.

28 m

3.

A park has a triangular flower bed with vertices at coordinates $(0, 0)$ , $(8, 0)$ , and $(4, 6)$ on a grid where each unit represents 1 meter.

1.

What is the area of the flower bed in square meters?

2.

What is the perimeter of the flower bed, rounded to the nearest tenth of a meter?

E

Error Analysis

1.

Maya solved this problem:

"A triangle has a base of 10 cm, a slant side of 13 cm, and a height of 12 cm. Find the area."

Maya's work:

$A = \frac{1}{2}(10)(13)$
$A = 65$ cm²

What error did Maya make, and what is the correct area?

A.

Maya used the slant side (13) instead of the perpendicular height (12). The correct area is 60 cm².

B.

Maya forgot to square the base. The correct area is 650 cm².

C.

Maya's answer of 65 cm² is correct.

D.

Maya should have used $A = bh = 10 \times 12 = 120$ cm².

2.

Kevin solved this problem:

"An equilateral triangle has side length 10. Find the height."

Kevin's work:

The altitude bisects the base, so half the base is $\frac{10}{2} = 5$ .
The height equals half the base, so $h = 5$ .

What error did Kevin make, and what is the correct height?

A.

Kevin assumed the height equals half the base. He should use the Pythagorean theorem: $h = \sqrt{10^2 - 5^2} = \sqrt{75} = 5\sqrt{3}$ .

B.

Kevin should have used $h = \frac{10\sqrt{2}}{2} = 5\sqrt{2}$ .

C.

Kevin's answer of h = 5 is correct.

D.

Kevin should have used $h = 10\sqrt{3}$ .

F

Challenge / Extension

1.

The area of an equilateral triangle is $25\sqrt{3}$ cm². What is the side length in centimeters?

2.