Question

19) Find the surface area of the solid shown that has a square base. 9 in 7 in 3 in​

Answer 1

The surface area of the composite shape is: 315 in.².

What is the Surface Area of the Composite Shape?

Surface area = surface area of square pyramid + surface area of square prism - 2(base area)

Surface area of square pyramid = Area of base + 1/2(perimeter of base × slant height) = 9² + 1/2[4(9) × 7] = 207 in.²

Surface area of square prism = 2a² + 4ah = 2(9²) + 4(9)(3)

Surface area of square prism = 2(9²) + 4(9)(3) = 270 in.².

Base area = 9² = 81 in.².

Surface area of the composite shape = 207 + 270 - 2(81) = 315 in.².

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Answer 2

Answer:

315 in.²

Step-by-step explanation:

Recall:

area of rectangle = length × width

area of triangle = base × height / 2

Base of prism: 9 in. × 9 in. = 81 in.²

4 sides of prism: 4 × 9 in. × 3 in. = 108 in.²

Lateral area of pyramid: 4 × 9 in. × 7 in. / 2 = 126 in.²

Total area = 81 in.² + 108 in.² + 126 in.² = 315 in.²