﻿ Area and Perimeter of Triangles Worksheets | Problems & Solutions Area and Perimeter of Triangles Worksheets

Area and Perimeter of Triangles Worksheets
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1.
What is the height of ΔPQR, if its area is 8 in.2 and the measure of QR is 4 in.?  a. 32 in. b. 4 in. c. 2 in. d. None of the above

Solution:

Area of triangle = 1 / 2 × base × height.
[Formula.]

8 = 1 / 2 × QR × PS
[Substitute the value of area of ΔPQR.]

QR × PS = 16
[Multiply each side by 2.]

4 × PS = 16
[Substitute QR = 4.]

PS = 4
[Divide each side by 4.]

So, height of the ΔPQR = 4 in.

2.
Find the perimeter of the equilateral triangle LMN.  a. 18 m b. 28 m c. 36 m d. 16 m

Solution:

Perimeter of the triangle LMN = LM + MN + NL
[Sum of all three sides.]

LM = MN = LN = 6 m
[Since LMN is an equilateral triangle.]

Perimeter = 6 + 6 + 6 = 18

So, the perimeter of ΔLMN is 18 m.

3.
Find the perimeter of the triangle PQR.  a. 48 cm b. 120 cm c. 55 cm d. 40 cm

Solution:

The perimeter of a triangle is the sum of all the lengths of the sides of the triangle.

From the figure, the lengths of the sides are 8 cm, 15 cm and 17 cm.

The perimeter of the triangle PQR = 8 + 15 + 17 = 40 cm

4.
Find the area of an equilateral triangle, if its perimeter and height are 30 cm and 5$\sqrt{3}$ cm respectively. a. 18 cm2 b. 36 cm2 c. 50$\sqrt{3}$ cm2 d. 25$\sqrt{3}$ cm2

Solution:

The perimeter of an equilateral triangle = 3 × base of the triangle

Base of the triangle = 30 ÷ 3 = 10 cm

The area of a triangle = 12 × base × height

= 12 × 10 × 53 = 253

So, the area of the triangle is 253 cm2.

5.
What is the area of the triangle?  a. 64 cm2 b. 88 cm2 c. 84 cm2 d. 45 cm2

Solution:

Base of the triangle = 12 cm and its height = 14 cm

Area of a triangle = 1 / 2 × base × height

= 1 / 2 × 12 × 14

= 84

Area of the triangle is 84 cm2.

6.
What is the area of the triangle?  a. 40 in.2 b. 80 in.2 c. 24 in.2 d. 36 in.2

Solution:

Base of the triangle = 20 in. and its height = 8 in.

Area of a triangle = 1 / 2 × base × height

= 1 / 2 × 20 × 8

= 80

So, area of the triangle is 80 in.2.

7.
Find the area of a triangle whose base is 9 in. and height is 10 in. a. 47 in.2 b. 45 in.2 c. 49 in.2 d. 44 in.2

Solution:

Area of a triangle = 1 / 2 × base × height

= 12 × 9 × 10
[Substitute base = 9 and height = 10.]

= 902 = 45
[Simplify.]

The area of the triangle is 45 in.2

8.
The area of a triangle is 12 in.2 and base of the triangle is 3 in. Find the height of the triangle. a. 9 in. b. 7 in. c. 8 in. d. 10 in.

Solution:

Area of triangle = 1 / 2 x base x height

12 = 12 x 3 x height
[Substitue the values of Area and Base.]

12 x 2 = 3 x height
[Multiply each side by 2.]

243 = height
[Divide each side by 3.]

8 = height

The height of the triangle is 8 in.

9.
Find the length ($b$) of the base of the triangle ABC in the figure, if area of the triangle ABC is 10 cm2.  a. 2 cm b. 4 cm c. 5 cm d. 6 cm

Solution:

The area of the triangle ABC = 1 / 2 x BC x AD .

12 x BC x AD = 10
[Substitute the value of the area of the triangle.]

[Multiply both sides by 2.]

BC x 4 = 20

BC = b = 5
[Divide each side by 4.]

The length of the base of the triangle ABC is 5 cm.

10.
Find the perimeter of the triangle ABC.  a. 12 cm b. 10 cm c. 14 cm d. 20 cm

Solution:

The perimeter of a triangle is the sum of all the lengths of the sides of the triangle.

From the figure, the lengths of the sides are 4 cm, 5 cm and 3 cm.

The perimeter of the triangle ABC = 4 + 5 + 3 = 12 cm