Question

1) Find the area of an equilateral triangle if length of each of it's sides is 12 cm.
2) Find the area of an isosceles triangle in length of it's equal sides are 10 cm each and length of it's third side is 16 cm ​

Answer 1

Given :

• In equilateral triangle, length of each of it's sides is 12 cm.

• In isosceles triangle, length of it's equal sides are 10 cm each and length of it's third side is 16 cm

To find :

• Area of an equilateral triangle
• Area of isosceles triangle

Solution :-

According to first question

• Length of each equal side of equilateral triangle = 12 cm

According to the given condition

→ Area of equilateral triangle

→ √3/4 × a² ( " a " is each side of equilateral triangle)

→ √3/4 × 12 × 12

→ √3 × 3 × 12

→ 36√3 cm²

Hence, area of equilateral triangle is 36√3 cm²

According to second question

• Length of each equal sides of isosceles triangle = 10cm
• Length of third side = 16 cm

Semiperimeter (s) = ½ (a + b + c)

Let

• a = 10cm
• b = 10cm
• c = 16cm

→ s = ½ (a + b + c)

→ s = ½ (10 + 10 + 16)

→ s = ½ × 36

→ s = 18

Now,

→ Area of isosceles triangle

→ √s(s - a)(s - b)(s - c)

→ √18(18 - 10)(18 - 10)(18 - 16)

→ √18 × 8 × 8 × 2

→ √18 × 64 × 2

→ √36 × 64

→ √2304

→ 48 cm²

Therefore,

• Area of isosceles triangle is 48 cm²