Question

10. Find the area of an equilateral triangle each of whose sides measures (i) 18 cm, (ii) 20 cm.​

Answer 1

Step-by-step explanation:

i). √3/4×a^2

√3/4×18^2

√3/4×324

√3×81

140.30 cm^2

ii). √3/4×a^2

√3/4×20^2

√3/4×400

√3×100

173.20 cm^2

Answer 2

Here,

We will use Heron's formula for finding area of each triangle. This is because height of triangle is not given.

Formula of heron's formula is :

Area of triangle = √s(s - a)(s - b)(s - c)

In which,

• a, b, and c are sides of triangle.
• s is semi-perimeter of triangle.

Formula for semi-perimeter is:

Semi-perimeter = Perimeter/2

(i) Side of an equilateral triangle is 18 cm.

18 cm is side of equilateral triangle. So, All sides of triangle are of 18 cm because all sides of equilateral triangle are equal.

So,

s = 18 + 18 + 18/2

s = 54/2

s = 27

Semi-perimeter = 27 m.

Area of triangle :

= √27 (27 - 18)(27 - 18)(27 - 18)

=√27 × 9 × 9 × 9

= √3 × 3 ×3 × 3 × 3 × 3 × 3 × 3 × 3

= 3 × 3 × 3 × 3 ×√3

= 81√3

Area of triangle is 81√3 cm².

_______________________________

(ii) Side of equilateral triangle is 20 cm.

Similarly, as first part :

All side measure of triangle is 20 cm.

So,

s = 20 + 20 + 20/2

s = 60/2

s = 30

Semi-perimeter = 30 cm.

Area of triangle:

= √30 (30 - 20)(30 - 20)(30 - 20)

= √30 × 10 × 10 × 10

= √2 × 5 × 3 × 2 × 5 × 2 × 5 × 2 × 5

= 2 × 2 × 5 × 5 × √3

= 100√3

Area of triangle is 100√3 cm².