# 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