Answer:
- volume: 42 cm³
- area: 96 cm²
Explanation:
You want the volume and surface area of a right triangular prism with base edge lengths of 3, 4, and 5 cm, and a prism height of 7 cm.
(a) Volume
The area of the triangular base of the prism is ...
A = 1/2bh = 1/2(4 cm)(3 cm) = 6 cm²
The volume of the prism is ...
V = Bh = (6 cm²)(7 cm) = 42 cm³
The prism has a volume of 42 cm³.
(b) Area
The total surface area is the sum of the areas of the two bases and the area of the three rectangular faces.
The area of one base is found above to be 6 cm², so both bases together will have an area of 2×6 cm² = 12 cm².
The lateral area of the rectangular faces is the product of the perimeter of the base and the height of the prism.
LA = Ph = (3 +4 +5 cm)(7 cm) = 84 cm²
The total surface area is the sum of these areas:
SA = 12 cm² +84 cm² = 96 cm²
The prism has an area of 96 cm².