Question

Find the area of an equilateral triangle with apothem of 5cm.

Answer 1

Area = 16.669 cm^2

Explanation:

An EQUILATERAL TRIANGLE has all it's sides and angles the same.

Sum of angles of a triangle = 180°

Each angle = 180°/3

= 60°

A= B = C = Angles

a = b = c = lengths of sides = unknown

The apothem is given as 5.

We'll call it h.

h = 5

From Trigonometry; SohCahToa

Sin 60° = opposite / Hypotenuse

sin 60° = h/b

0.866° = 5/b

b = 5/0.866°

b = 5.774 cm

Let's solve for AREA.

AREA = 1/2 * Base * Height

A = 1/2 * 5.774 * 5.774

A = 1/2 * 33.339

A = 16.669 cm ^2

Please find the attached file

Math is fun

Answer 2

16.64645cm²

Explanation:

All of the angles are equal: A = B = C = 180/3 = 60°.

All of the sides are equal: a = b = c.

h = 5 cm, sin60 = h/a = 5/a, a = 5/sin60 = 5.77 cm.

Area = 1/2bh = 1/2 x 5.77 x 5.77 = 33.2929/2 = 16.64645cm²