Answer:
The surface area of the triangular prism is 136 units²
Step-by-step explanation:
The surface area of a prism is the sum of areas of its faces
From the attached figure
The shape is a triangular prism, it has 5 faces
- Two triangular faces with base 6 units and height 4 units
- Two rectangular faces with dimensions 7 units and 5 units
- One rectangular face with dimensions 7 units and 6 units
Lets find the area of the 5 faces
Area of the 2 triangular faces
∵ The area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
∵ The base = 6 units
∵ The height = 4 units
∴ The area of each triangular face = [tex]\frac{1}{2}[/tex] × 6 × 4
∴ The area of each triangular face = 12 units²
Area of the 2 rectangular faces with dimensions 7 units and 5 units
∵ The area of a rectangle = length × width
∵ The length = 7 units
∵ The width = 5 units
∴ The area of the rectangular face = 7 × 5
∴ The area of each rectangular face = 35 units²
Area of the rectangular face with dimensions 7 units and 6 units
∵ The area of a rectangle = length × width
∵ The length = 7 units
∵ The width = 6 units
∴ The area of the rectangular face = 7 × 6
∴ The area of the rectangular face = 42 units²
∵ The surface area = sum of areas of all faces
∴ The surface area = 12 + 12 + 35 + 35 + 42
∴ The surface area = 136 units²
The surface area of the triangular prism is 136 units²
