**Heron’s Formula Class 9 Worksheet with Answers**

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**Heron’s Formula Class 9 Worksheet with Answers**

**1.** Find the length of each side of an equilateral triangle having an
area of 9√3 𝑐𝑚^{2}.

**2.** Find the area of an isosceles triangle having base 2 cm and the
length of one of the equal sides 4 cm.

**3.** How many times area is changed, when sides of
a triangle are doubled.

**4.** If the perimeter of an isosceles triangle is 11 cm and its base
is 5 cm, its area is 5√11𝑐𝑚^{2}.
State true or false and give reason.

**5.** If the area of an equilateral triangle is 16√3 𝑐𝑚^{2},
then find the perimeter of the triangle.

**6.** The cost of levelling a ground in the form of a triangle having
the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per 𝑚^{2}
is ₹ 918. State whether the statement is true or false and justify your
answer.

**7.** The perimeter of an isosceles triangle is 32 cm. The ratio of the
equal side to its base is 3 : 2. Find the area of the triangle.

**8.** The lengths of the sides of a triangle are 7
cm, 13 cm and 12 cm. Find the length of perpendicular from the opposite vertex
to the side whose length is 12 cm.

**9.** The perimeter of a triangle is 50 cm. One side of a triangle is 4
cm longer than the smaller side and the third side is 6 cm less than twice the
smaller side. Find the area of the triangle.

**10.** The area of a trapezium is 475 𝑐𝑚2
and the height is 19 cm. Find the lengths of its parallel sides if one side is
4 cm greater than the other.

**11.** If each side of a triangle is doubled, then find the ratio of
area of new triangle thus formed and the given triangle.

**ANSWERS**

** **

**1.** a = 6 cm

**2.** √15 𝑐𝑚^{2}

**3.** Four times

**4.** True

**5.** 24 cm

**6.** True

**7.** 32√2 𝑐𝑚^{2}

**8.** 4√3 𝑐𝑚

**9.** 109.6 𝑐𝑚^{2}

**10.** 23 cm, 27 cm

**11.** 4 : 1

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