Answer:
7) 42
8) 358
9) 320
10) 288
Step-by-step explanation:
Problems 7, 8, and 10 all use the same formula: the formula for the surface area of a rectangular prism.
Formula: 2 * (lw + lh + hw)
where l = length, w = width and h = height
This is a condensed form of the sum lw + lw + lh + lh + hw + hw where each product is a face of the prism.
replace each variable in the formula above with the values given in your problems for 7, 8 and 10:
7) 2 * (3*3 + 3*2 + 2*3) = 2 * (9 + 6 + 6) = 2 (21) = 42
8) 2 * (12*7 +12*5 + 5*7) = 2 * (84 + 60 + 35) = 2(179) = 358
10) 2* (12*4 + 12*6 + 4*6) = 2 * (48 + 72 + 24) = 2(144) = 288
Now 9 is a little different, as it contains a regular pentagon. However it is not much different from the other problems as it is also a prism.
The formula for the area of any regular polygon can be in the form:
Area = ap where the a stands for apothem (which is the distance from the center of a regular polygon to its side, in this case it is 5.5 yds) and the p is the perimeter of the polygon.
The reason for this formula involves the polygon being divided into as many congruent triangles as it has sides, but that is for another time : )
Given this formula for the area of the pentagon, you can substitute values:
Area = (5.5)(number of sides * length of a side)
Area = (5.5)(5 * 8) = 110
And get that the area of the face is 110 yd^2
the rest of the faces are rather straightforward as they contain rectangles of sides 4 yds and 5 yds, and you would end up with 5 of them (for each side of the pentagon)
Therefore by adding up each of the bases and the sides, you should get:
110 + 110 + 20 + 20 + 20 + 20 + 20 = 320
Hope that helped : )