Question - Calculating Surface Area of Composite 3D Figure
Solution:
To find the surface area of the 3D figure provided in the image, you need to calculate the area of each visible surface and then add them all together.The figure is a composite solid made up of two rectangular prisms. We must be careful not to double-count any area that is shared between the two prisms.1. The large, vertical front face is 16 in. by 16 in., so its area is $$16\ in \times 16\ in = 256\ in^2$$.2. The top face of the larger prism is 16 in. by 8 in., so its area is $$16\ in \times 8\ in = 128\ in^2$$.3. The back face of the larger prism, which is identical to the front, is also $$16\ in \times 16\ in = 256\ in^2$$.4. The bottom face of the larger prism is identical to the top face and has an area of $$16\ in \times 8\ in = 128\ in^2$$.5. The left face of the large prism is 16 in. by 8 in., giving an area of $$16\ in \times 8\ in = 128\ in^2$$.Now let's consider the smaller, attached prism:6. The visible part of the right side of the larger prism is an 8 in. by 8 in. square (above the smaller prism), with an area of $$8\ in \times 8\ in = 64\ in^2$$.7. The front face of the smaller prism is 6 in. by 8 in., giving an area of $$6\ in \times 8\ in = 48\ in^2$$.8. The top face of the smaller prism (visible portion) is 6 in. by 8 in., with an area of $$6\ in \times 8\ in = 48\ in^2$$.9. The right-side face of the smaller prism (aligned with the front face of the larger prism) is 6 in. by 16 in., with an area of $$6\ in \times 16\ in = 96\ in^2$$.Now let's add up all these areas to find the total surface area:$$256\ in^2 + 128\ in^2 + 256\ in^2 + 128\ in^2 + 128\ in^2 + 64\ in^2 + 48\ in^2 + 48\ in^2 + 96\ in^2 = 1152\ in^2$$.So the total surface area of the figure is 1,152 square inches.
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