Question

What is the area, in square centimeters, of an equilateral triangle with a perimeter of 15 centimeters? Round the answer to the nearest tenth.

Answer 1

10.8 cm^2 to nearest tenth.

Explanation:

You can use Hero's formula to do this:

Area = √[s(s-a)(s-b)(s-c)] where s = semi-perimeter, a b and c are the lengths of the 3 sides,

Here s = 15/2 = 7.5 and a, b and c = 5.

area = √(7.5 * 2.5 * 2.5 * 2.5)

= √117.1875

= 10.8253.

Another method would be to use trigonometry

h = 5 sin 60 and 1/2 * base = 1/2 * 5 = 2.5

So area = 5 sin60 * 2.5 = 10.8253,

Answer 2

A≈10.83cm²

Explanation:

Unit Conversion:

P=15cm

Using the formulas

A=3

4a2

P=3a

Solving forA

A=3P2

36=3·152

36≈10.82532cm²