Question

question 14 of 25
what is the surface area of the right prism given below?
a. 520 units²
b. 600 units²
c. 350 units²
d. 1200 units²

Explanation:

Step1: Calculate the area of the two triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 12\), \(h=5\). So, \(A_{triangle}=\frac{1}{2}\times12\times5 = 30\). The area of two triangular bases is \(2\times30=60\).

Step2: Calculate the area of the three rectangular faces

• For the face with dimensions \(12\times10\): \(A_1 = 12\times10=120\)
• For the face with dimensions \(13\times10\): \(A_2=13\times10 = 130\) (using Pythagoras \(a=\sqrt{12^{2}+5^{2}} = 13\))
• For the face with dimensions \(15\times10\): \(A_3=15\times10=150\)

Step3: Sum up all the areas

The surface area \(S=60 + 120+130+150=520\)

Answer:

A. 520 units²