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.
<u>3 congruent triangles</u>:
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
<u>3 congruent rectangles</u>:
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
<u>1 base triangle</u>:
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.
