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## Chapter 12: Heron’s Formula

Very Short Answer Type Questions: [1 Mark]

1. The length of the sides of a triangle is 5x, 5x and 8x. Find the area of the triangle.

Sol.

∴ Area of the triangle

2. Find the area of the triangle having sides 1 m, 2 m and 2 m.

Sol.

3. The sides of a triangular flower bed are 5 m, 8 m and 11 m. Find the area of the flower bed.

Sol.

∴ Area of the triangle

4. Each equal side of an isosceles right triangle is x cm. Find its area.

Sol. Area of the triangle = 1/2 × x × x cm2

= x2 /2 cm2

5. Find the area of an equilateral triangle of side 10 cm.

Sol. Area of the triangle = (10) 2/4 × √3 cm= 25 √3 cm2

6. The length of the sides of a triangle is 5 cm, 7 cm and 8 cm. Find the area of the triangle.

Sol.

7. Find the area of an equilateral triangle of side 2 cm.

Sol. Area of the triangle = 22 × √3 /4 cm2 =√3 cm2

8. The sides of a triangle are 56 cm, 60 cm and 52 cm long. Find the area of the triangle.

Sol.

∴ Area of the triangle

9. The base of a right triangle is 8 cm and the hypotenuse is 10 cm. What is its area?

Sol. The altitude of the triangle

= 6 cm

∴ Area of the triangle = 1/2 × 8 × 6 cm2 = 24 cm2

10. An isosceles right triangle has area 8 cm2. Find the length of its hypotenuse.

Sol. We have, 1/2 × x × x = 8 ⇒ x = 4

∴ The hypotenuse of the triangle

11. The base and corresponding altitude of a parallelogram are 10 cm and 3.5 cm respectively. Find the area of the parallelogram.

Sol. Area of the parallelogram

= 2 × area of ΔABD

= 2 × 1/2 × AB × DE = 10 × 3.5 cm2 = 35 cm2

12. Find the area of a regular hexagon of side a.

Sol.

Area of the regular hexagon ABCDEF

= 6 × area of the equilateral triangle AOB

13. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs3 per m2.

= 54 m

Area of the triangle

Required cost of leveling = Rs 3x 306 = Rs 918

14. Two adjacent sides of a parallelogram are 74 cm and 40 cm. If one of its diagonals is 102 cm. Find the area of the parallelogram.

Sol.

Area of ||gm ABCD = 2 × Area of DABC

In DABC,

Area of ||gm = 2 × 1224 cm2 = 2448 cm2.

15.In the figure, ABCD is a rectangle and DEC is an equilateral triangle. Find the area of ΔDEC.

Sol. Area of ΔDEC = 62 × √3/ 4 cm2= 9 √3 cm2

16. If the perimeter of a rhombus is 20 cm and one of the diagonals is 8 cm. Find the area of the rhombus.

Sol. The perimeter of a rhombus = 20 cm.