a triangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square centimeters. find its slant height
Accepted Solution
A:
we know that [surface area of a triangular pyramid]=[area of the base]+3*[area of the lateral triangle]
step 1 find the area of the base is a equilateral triangle applying the Pythagorean theorem
h²=10²-5²------> h²=100-25----------> h=√75 cm [area of the base]=10*√75/2---------> 5√75 cm²
step 2 find the area of the lateral triangle [surface area]=[area of the base]+3*[area of the lateral triangle] [area of the lateral triangle]={[surface area]-[area of the base]}/3 [area of the lateral triangle]={[214.5]-[5√75]}/3 [area of the lateral triangle]=57.07 cm²
step3 find the slant height [area of the lateral triangle]=b*[slant height]/2 [slant height]=2*[area of the lateral triangle]/b [slant height]=2*[57.07]/10-----> [slant height]=11.41 cm