#### Class nine Mathematics Chap 12 Heron Formula Extra Questions

## 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 cm^{2}

= x^{2} /2 cm^{2}

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

**Sol. **Area of the triangle = (10) ^{2}/4 × √3 cm=
25 √3 cm^{2}

**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 = 2^{2}
× √3
/4 cm^{2} =√3 cm^{2}

**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 cm^{2} = 24 cm^{2}

**10. ****An isosceles right triangle has area 8
cm ^{2}. 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 cm^{2} = 35 cm^{2}

**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 m ^{2}.**

**= 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 cm^{2} = 2448
cm^{2}.

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

**Sol. **Area of ΔDEC = 6^{2} × √3/ 4 cm^{2}= 9 √3 cm^{2}

**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.