Answer:
- Surface Area = 26.88 cm²
- Volume = 7.68 cm³
Step-by-step explanation:
The given shape is a right triangular prism
Surface Area
It has 5 surfaces and these are the calculations for each of the four surfaces
- Two triangles each with base b = 3.2 cm and height h = 2.4 cm
Each triangle has an area of 1/2 x b x h = 1/2 x 3.2 x 2.4 = 3.84 cm²
So both triangles will have surface area of 2 x 3.84 = 7.68 cm²
- Bottom base of the prism is a rectangle with length = 3.2 cm and width = 2.0 cm
Area of this rectangle = 3.2 x 2.0 = 6.4 cm²
- The vertical side of the prism is also a rectangle with length = 2.4 cm and width = 2 cm. The area of this rectangle is 2.4 x 2 = 4.8 cm²
- The lateral side (sloping surface) is also a rectangle of dimensions 4 cm x 2 cm and its area = 4 x 2 = 8 cm²
- Total surface area of prism = 7.68 + 6.4 + 4.8 + 8 = 26.88 cm²
Volume
- The volume of the prism is one-half the area of a rectangular prism with the same dimensions . If you stack up the inverted triangular prism on to the same prism you will get a rectangular prism
- The volume of a rectangular prism of dimensions 2.4 x 3.2 x 2.0 = 15.36 cm³
- So one-half of this area = 15.36/2 = 7.68 cm³
