Question

what is the area rounded to the nearest 10th of square inch of an equal lateral triangle that has a perimeter of 24 inches

Answer 1

A = 27.7

Explanation:

Knowing that an equilateral triangle has 3 equal side lengths, we can create our area and perimeter equations! x will be one of the side lengths

• P = x + x + x

• P = 3x

• A = (1/2)(b*h)
• all angles are 60
• Using angles: sin(60) =
  `(√(3) )/(2) = (opp)/(adj) = (h)/(a)`
• A =
  `a^(2) (√(3) )/(4)`

P = 3x = 24

x = 8

A =
`8^(2) (√(3) )/(4)`

A = 27.7