Find the surface area and volume of the composite figure.

Mathematics

1 answer:

Shalnov [3]3 years ago

6 0

Answer:

The total volume is 33.6 + 107.52 = 141.12

The total surface area is 52 + 22.4 + 76.8 + 26.88 = 178.08

Step-by-step explanation:

Top prism:

To find the volume of the top prism, multiply the area of the base by the height. This is 1/2 times width times height times length.

V =1/2 l*w*h =1/2* 3*2.8*8 = 33.6

To find the surface area of a prism, find the area of the triangular base and the area of each rectangular side.

Area of the base is A = 1/2 * b*h = 1/2 * 3 * 8 = 12. Since there are 2 bases, the area is 24.

Area of the rectangular side is A = b*h = 2.8*5 = 14. Since there are two, the area is 2*14 = 42.

The surface area of the prism is 24 + 28 = 52.

Bottom prism:

To find the volume of the bottom prism, multiply the width times the height times the length.

V = l*w*h = 8*2.8*4.8 = 107.52

To find the surface area of the bottom prism, find the area of the base and each side of the house.

A = 8*2.8 = 22.4

A = 8*4.8 = 38.4 which occurs twice so it has a total area of 76.8

A = 2.8*4.8 = 13.44 which occurs twice so it has an area of 26.88.

The total volume is 33.6 + 107.52 = 141.12

The total surface area is 52 + 22.4 + 76.8 + 26.88 = 178.08

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