SOLUTION: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.

Question 363105: Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.

area A of a triangle = 1/2 * base b * height h
P perimeter triangle = 21 inches
length of one side of equilateral triangle = 21/3 = 7 inches
an equilateral triangle is made up of 2 right triangles
in this case each has a base of 7/2 = 3.5 inches,
and each has an hypotenuse of 7 inches
find the height using Pythagorean Theorem
(7/2)^2 + h^2 = 7^2
49/4 + h^2 = 49
49/4 + h^2 = 196/4
h^2 = 147/4 = (49 * 3)/4
h = (7sqrt(3))/2 inches
area A = 1/2 * 7 * (7sqrt(3))/2
A = (49sqrt(3))/4 = 21.2 square inches rounded to nearest tenth

RELATED QUESTIONS
Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the... (answered by Earlsdon,mananth,Fombitz)

Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the... (answered by jessica43)

Find the length and width of a rectangle that has area 55 square centimeters and a... (answered by josmiceli)

Solve the following problem. Be sure to make a diagram of the situation with all the... (answered by josgarithmetic,MathTherapy)

Find the measure of one exterior angle of a regular polygon that has 21 sides. Round... (answered by w_parminder)

Find the perimeter of an equilateral triangle whose area is equal to that of a triangle... (answered by math_tutor2020)

the perimeter of an equilateral triangle is 21 inches. find the length of the... (answered by drj)

The area of a triangle is 50 square inches. Find the length of the side included between... (answered by josgarithmetic)

Find the area of the triangle having the indicated angle and sides. (Round your answer to (answered by lwsshak3)