Question

Given: SP = PT=ST=2.6. Find: V Un S # 1 # O is centroid of ASPT, MOL(SPT). m/MPO = 70° M 0 T​

Answer 1

Since O is the centroid of ASPT, it divides each median in the ratio 2:1. Therefore, OS = 2/3 * 2.6 = 1.7.

The area of triangle SPT is (1/2) * 2.6 * 2.6 = 3.36.

The area of triangle MPO is (1/2) * 1.7 * 2.6 = 2.22.

The area of triangle OSP is (1/2) * 1.7 * 1.7 = 1.54.

The area of triangle OPT is (3.36 - 2.22 - 1.54) = 0.58.

Therefore, V = 3.36 + 2.22 + 1.54 + 0.58 = 7.6.