Question

Find the surface area of the composite solid. Write your answer as a decimal.

Answer 1

Answer:

283.5 cm squared

Step-by-step explanation:

The surface area of a solid is basically just the sum of the areas of all the exterior sides. In this figure, we have 3 congruent triangles at the top, 3 congruent rectangles on the sides, and 1 triangle at the base. We need to find all these areas.

3 congruent triangles:

The area of a triangle is denoted by: A = (1/2) * b * h, where b is the base and h is the height.

Here, the base of one triangle is 10 and the height is 4. So:

A = (1/2) * b * h

A = (1/2) * 10 * 4 = 20

Since there are 3 such triangles, multiply 20 by 3:

20 * 3 = 60 cm squared

3 congruent rectangles:

The area of a rectangle is denoted by: A = lw, where l is the length and w is the width.

Here, the length is 6 and the width is 10, so:

A = lw

A = 6 * 10 = 60

There are 3 such rectangles, so multiply 60 by 3:

60 * 3 = 180 cm squared

1 base triangle:

Again we use the formula A = (1/2) * b * h for this area.

Here, the base is 10 and the height is 8.7, so:

A = (1/2) * b * h

A = (1/2) * 10 * 8.7 = 43.5 cm squared

Add all these together:

60 + 180 + 43.5 = 283.5 cm squared

The answer is thus 283.5 cm squared.

Answer 2

Answer:

283.5 cm²

Step-by-step explanation:

3 rectangles + 3 triangles on top + triangular base

3(10×6) + 3(½×10×4) + (½×10×8.7)

180 + 60 × 43.5

283.5 cm²