Question

a triangular prism has a base area of 15 cm² and a perimeter of 10 cm. if the height of the prism is 12 cm, what is the surface area? a. 180 cm² b. 120 cm² c. 150 cm² d. 195 cm²

Explanation:

Step1: Calculate the lateral surface area

The formula for the lateral surface area of a prism is \(LSA=\text{Perimeter of base}\times\text{Height of prism}\).
Given perimeter of base \(P = 10\space cm\) and height of prism \(h=12\space cm\), so \(LSA = 10\times12=120\space cm^{2}\).

Step2: Calculate the total surface area

The formula for the total surface area of a prism is \(TSA = LSA+2\times\text{Base Area}\).
Given base area \(B = 15\space cm^{2}\), so \(TSA=120 + 2\times15\).
First, calculate \(2\times15 = 30\). Then \(TSA=120+30\).

Answer:

\(150\space cm^{2}\), so the answer is c.