Worksheet on Area of Triangle for Class 12

Solved Questions on Area of Triangle

1. Find the area of a triangle with sides of lengths 6 cm, 8 cm and 10 cm using Heron's formula.

a) 20 cm²
b) 22 cm²
c) 24 cm²
d) 26 cm²

Answer: c) 24 cm²

Explanation: To find the area using Heron's formula, we first need to calculate the semi-perimeter "s":
a = 6 cm
b = 8 cm
c = 10 cm
s = (6 + 8 + 10) / 2
= 24 / 2
= 12 cm

Now, we can use Heron's formula to find the area:

Area = √[12 x (12 - 6) x (12 - 8) x (12 - 10)]
Area = √(12 x 6 x 4 x 2)
Area = √(576)
Area = 24 cm²

2. Find the area of an equilateral triangle with each side measuring 10 meters.

a) 25√3 cm²
b) 15√3 cm²
c) 10√3 cm²
d) 5√3 cm²

Answer: a) 25√3 cm²

Explanation: Side = 10 cm
Thus its
A = (√3)/4 × side²
Area = √3/4 × 10²
= 25√3 cm²

3. In a right-angled triangle, the height of the triangle is 17 cm and the base is 8 cm. Find the area of the triangle.

a) 50 cm²
b) 52 cm²
c) 64 cm²
d) 68 cm²

Answer: d) 68 cm²

Explanation: Height = 17 cm, Base = 8 cm
Thus its
Area of a right-angled triangle = 1/2 × Base × Height
A = 1/2 × 17 x 8
= 17 x 4
= 68 cm²

4. The sides of a triangle are in the ratio 3 : 4 : 5 and the perimeter is 36 units. Find the area of the triangle.

a) 50 square units
b) 52 square units
c) 54 square units
d) 56 square units

Answer: c) 54 square units

Explanation: Let the sides be 3x, 4x, and 5x (where x is a common factor).
Perimeter = 3x + 4x + 5x
= 12x = 36 units
x = 36 / 12
= 3 units

The sides are 3x = 3 x 3 = 9 units, 4x = 4 x 3 = 12 units, and 5x = 5 x 3 = 15 units.

Using Heron's formula:
Semi-perimeter (s) = (9 units + 12 units + 15 units) / 2
= 36 units / 2
= 18 units

Area = √(18 units x (18 units - 9 units) x (18 units - 12 units) x (18 units - 15 units))
Area = √(18 units x 9 units x 6 units x 3 units)
= √(2916 square units)
= 54 square units

5. Find the area of a triangle with the height is 16 cm and the base is 10 cm.

a) 80 cm²
b) 82 cm²
c) 84 cm²
d) 86 cm²

Answer: a) 80 cm²

Explanation: Area of a triangle = 1/2 × Base × Height
A = 1/2 × 10 x 16
= 5 x 16
= 80 cm²

Practice Questions on Area of Triangle

1. Find the area of a triangle with a base length 10 cm and height 6 cm.

a) 30 cm²
b) 32 cm²
c) 34 cm²
d) 36 cm²

Answer: a) 30 cm²

2. Find the area of a triangle with a base length 18 cm and height 14 cm.

a) 126 cm²
b) 132 cm²
c) 134 cm²
d) 136 cm²

Answer: a) 126 cm²

3. Find the area of a triangle with a base length 20 cm and height 16 cm.

a) 100 cm²
b) 120 cm²
c) 140 cm²
d) 160 cm²

Answer: d) 160 cm²

4. Calculate the area of a triangle whose sides are 12 cm, 6 cm and 15 cm.

a) 50.6 cm²
b) 42.6 cm²
c) 34.2 cm²
d) 16 cm²

Answer: c) 34.2 cm²

5. Determine the area of a triangle with side lengths 18 cm and 10 cm and a perimeter of 42 cm.

a) 20.6 cm²
b) 82.6 cm²
c) 44.2 cm²
d) 69.7 cm²

Answer: d) 69.7 cm²

6. Find the area of the scalene triangle whose sides are 5 cm, 6 cm and 7 cm.

a) 2√6 cm²
b) 8√6 cm²
c) 4√6 cm²
d) 6√6 cm²

Answer: d) 6√6 cm2

7. Find the area of a triangle with a base length 12 cm and height 10 cm.

a) 60 cm²
b) 62 cm²
c) 64 cm²
d) 66 cm²

Answer: a) 60 cm²

8. Find the area of a triangle with base length 22 cm and height 10 cm.

a) 110 cm²
b) 112 cm²
c) 124 cm²
d) 136 cm²

Answer: a) 110 cm²

9. Calculate the area of a right-angle triangle with base b = 4 cm and hypotenuse H = 10 cm.

a) 10 cm²
b) 12 cm²
c) 14 cm²
d) 16 cm²

Answer: b) 12 cm²

10. Find the area of a triangle with base length 44 cm and height 30 cm.

a) 660 cm²
b) 662 cm²
c) 664 cm²
d) 666 cm²

Answer: a) 660 cm²