Equilateral Triangle Area

Question

The height of an equilateral triangle is 98 ft how do I solve

Answer 1

The height of an equilateral triangle is 22 feet, what is the area of the triangle?

Equilateral triangles have all three angles are equal and all three sides are equal.....

so that means every angle in the triangle is 60 or 3 * 60 = 180

The height of the triangle is equal to a vertical altitude running from on vertex to midpoint of one of the legs forming one of two "30-60-90 right triangle"....the altitude (height) is one leg of this triangle so....

tan 30 = opp/side = x/22 let x = 1/2 length of the base of the triangle...so

x = 22 tan 30 = 12.70 cm so the base of the triangle is 2x = 2 * (12.70) = 25.40

A = 1/2 (b*h) or A= 1/2 (25.40)(22) = 279.43 ft²

.....Check using pythagorean theorem

a²+b² = c².......(12.70)^2 + (22)^2 = (25.40)^2......161.29 + 484 = 645.16

note...values are approximate to rounding to the nearest hundredth....