Which of the following represents the exact area, in square inches, of an equilateral triangle whose sides have a length of 10 inches? Group of answer choices 10 square 3 50 square 2 25 square 3 25 square 2

A = B = C = 60°

a = b = c

a = 10 in

K = 43.3013 in2

P = 30 in

s = 15 in

h = 8.66025 in

Step-by-step explanation:

Formulas and Calculations for a equilateral triangle:

Perimeter of Equilateral Triangle: P = 3a

Semiperimeter of Equilateral Triangle: s = 3a / 2

Area of Equilateral Triangle: K = (1/4) * √3 * a2

Altitude of Equilateral Triangle h = (1/2) * √3 * a

Angles of Equilateral Triangle: A = B = C = 60°

Sides of Equilateral Triangle: a = b = c

1. Given the side find the perimeter, semiperimeter, area and altitude

a is known; find P, s, K and h

P = 3a

s = 3a / 2

K = (1/4) * √3 * a2

h = (1/2) * √3 * a

2. Given the perimeter find the side, semiperimeter, area and altitude

P is known; find a, s, K and h

a = P/3

s = 3a / 2

K = (1/4) * √3 * a2

h = (1/2) * √3 * a

3. Given the semiperimeter find the side, perimeter, area and altitude

s is known; find a, P, K and h

a = 2s / 3

P = 3a

K = (1/4) * √3 * a2

h = (1/2) * √3 * a

4. Given the area find the side, perimeter, semiperimeter and altitude

K is known; find a, P, s and h

a = √ [ (4 / √3) * K ] = 2 * √ [ K / √3 ]

P = 3a

s = 3a / 2

h = (1/2) * √3 * a

5. Given the altitude find the side, perimeter, semiperimeter and area

h is known; find a, P, s and K

a = (2 / √3) * h

P = 3a

s = 3a / 2

K = (1/4) * √3 * a2