Question

9.9 If the height of an equilateral triangle is 12 cm, then what is the area of the triangle?​

Answer 1

Answer:

1/2 *12*12

72cm^2

hope it helos

Answer 2

Construction :

• Draw a equilateral triangle ∆ABC, with side = 2a
• Draw a line from A to D ( midpoint of BC) , such that AD is perpendicular to BC

Given :

• Height of equilateral triangle = 12cm

To find :

Area of triangle

Solution :

First of all we need to find out side of equilateral triangle.

As AD is perpendicular to BC, ∆ADB is a right angle triangle.

Therefore using Pythagoras theorem in ∆ADB, we get;

AB² = BD² + AD²

[ Note -

1. AB = 2a
2. BD = BC/2 = a ]

➝ (2a)² = (a)² + (12)²

➝ 4a² = a² + 144

➝ 4a² - a² = 144

➝ 3a² = 144

➝ a² = 144/3

➝ a² = 48

➝ a = √48

➝ a = ± 6.93

As a denotes side , it can't be negative

➝ a = 6.93

_______________________________

Now , we know that

• BC = 2a

➝ BC = 2(6.93) cm

➝ BC = 13.86 cm

• Also, AD = 12cm

Now , using Formula

Area of triangle = (1/2) × Base × Altitude

➝ Area of triangle = (1/2) × (BC) × (AD)

➝ Area of triangle = (1/2) × (13.86 cm) × (12 cm)

➝ Area of triangle = 83.16 cm²

______________________________

ANSWER : 83.16 cm²