Question

for a triangular prism, how do you find the area of the base (b)?
a. ( b=\frac{1}{2}\times \text{base}\times \text{height} )
b. ( b = 2\times \text{base}\times \text{height} )
c. ( b=\text{base}\times \text{height} )
d ( b=\frac{1}{2}\times \text{base}+\text{height} )

Explanation:

Step1: Recall the area formula of a triangle

The base of a triangular prism is a triangle. The area formula for a triangle is \(A=\frac{1}{2}\times\text{base}\times\text{height}\).

Step2: Match with the given options

Option a: \(B = \frac{1}{2}\times\text{base}\times\text{height}\) matches the area formula of a triangle.
Option b: \(B = 2\times\text{base}\times\text{height}\) is incorrect as it has an extra factor of 2.
Option c: \(B=\text{base}\times\text{height}\) is the area formula for a parallelogram (not a triangle).
Option d: \(B=\frac{1}{2}\times\text{base}+\text{height}\) is an incorrect combination (addition instead of multiplication).

Answer:

A. \(B=\frac{1}{2}\times\text{base}\times\text{height}\)