a triangular prism has bases with three congruent sides, each measuring 4 feet. the height of each triangle…
a triangular prism has bases with three congruent sides, each measuring 4 feet. the height of each triangle is approximately 3.5 feet. the distance between the triangular bases is 7 feet. what is the lateral area of the prism? 73.5 feet 73.5 square feet 84 feet 84 square feet
Answer
Explanation:
Step1: Identify lateral - face shape
The lateral faces of a triangular prism are rectangles.
Step2: Determine the dimensions of lateral - face rectangles
Each lateral - face rectangle has a length equal to the distance between the bases ($l = 7$ ft) and a width equal to the side length of the triangular base ($w = 4$ ft).
Step3: Calculate the area of one lateral - face rectangle
The area of a rectangle is $A_{rect}=l\times w$. For one lateral - face rectangle, $A_{1}=7\times4 = 28$ square feet.
Step4: Find the number of lateral - face rectangles
A triangular prism has 3 lateral - face rectangles.
Step5: Calculate the lateral area of the prism
The lateral area $L$ of the prism is $L = 3\times A_{1}$. So, $L=3\times28=84$ square feet.
Answer:
84 square feet