Question

Tom was playing with wooden blocks. He placed cubes on top of rectangular prisms to create composite shapes as shown below. Then, Tom was interested in finding out the surface area of each composite shape. Find the surface area of the composite shape composed of a cube with sides of 9 in placed on top of a rectangular prism with a length of 14 in, width of 11 in, and height of 4 in. Enter the missing part of the answer. Surface area of the cub= 486 in². Total surface area of the cube and the rectangular prism = 994 in². Overlapping area = 162 in². Surface area of the composite shape = □32 in² *

Answer 1

Answer: 832 inches squared.

Explanation:

Composite shapes' surface areas can be found by taking the individual geometrical shapes' surface areas. After doing so, add together the surface area, but make sure to subtract any overlapping area.

For this instance, you have a cube placed on top of a rectangular prism.

A cube's surface area is defined as
`A = 6a^(2)`., in which
`a` is defined as the side length of the cube.

A rectangular prism's surface area is defined as
`A=2(wl+hl+hw)`, in which the side lengths of the width, length, and height are used as W, L, and H.

The cube's surface area when the side length is 9 inches is 6 * (9)^2, or 486 inches squared.

The rectangular prism's surface area when side lengths are 14, 11, and 4 inches is A = 2(11*14 + 4*14 + 11*4), or 508 inches squared.

To calculate the composite area, the areas of the overlapping sections must be subtracted. Because there is a 9x9 area on the cube and a 9x9 area on the prism overlapping, you must subtract 2* (9)^2, or 162 inches squared, from the total area of 994 inches.

994 - 162 = 832 inches squared.