Answer:
16. 228 sq. ft.
17. 98 sq. yd.
18. 141.37 sq. m.
Explanation:
16.
Surface Area is the area of all the surfaces summed up.
In this figure, there are 4 sides (squares) and 1 bottom (square) and the top is 4 triangles.We have to sum up all of them to find total surface area.
Area of Square is side * side
So,
4 sides Area = 4 (6 * 6) = 4 * 36 = 144
Bottom Area = 6 * 6 = 36
Area of Triangle = 0.5 * base * height
So,
4 Triangle Area = 4 (0.5 * 6 * 4) = 4(12) = 48
Total Surface Area = 144 + 36 + 48 = 228 sq. ft.
17.
This figure has:
Bottom Rectangle
Left Side Rectangle
Front Triangle
Back Triangle
Little Rectangle to the Right
Slanted Rectangle Top
We find each area and sum.
Remember:
Area of Triangle = 0.5 * base * height
Area of Rectangle = base * height
So, we have:
Bottom = 8 * 2 = 16
Left Rect = 6 * 2 = 12
Front Triangle = 0.5 * 6 * 8 = 24
Back Triangle = same as front = 24
Little Rectangle to the Right = 2 * 1 = 2
Slanted Rectangle Top = 10 * 2 = 20
Now,
Total Surface Area = 16 + 12 + 24 + 24 + 2 + 20 = 98 sq. yd.
18.
This composite figure has a left side code (smaller one) and a right side cone (larger one).
We need to find "lateral surface area of cone" since we don't need the base.
The formula is:
Lateral Surface Area of Cone = pi * r * l
WHere
r is radius and l is slant height given
Larger Cone:
pi * 3 * 10 = 30 pi
Smaller Cone:
pi * 3 * 5 = 15 pi
Total Surface Area = 30 pi + 15 pi = 45 pi or 141.37 sq. m.