1)
Lateral area is the surface area, minus the bases. The area of a square is base times height. The lateral area is 112 centimeters squared, and the surface area is 336 centimeters squared.
2)
The bases of prisms are the triangles. The lateral area of the prism is 695 meters squared. The area of a triangle is base times height divided by 2. The surface area of the prism is 727 meters squared.
3)
The area of a circle is pir^2. The surface area of the cylinder is 1,230 inches cubed.
4)
The area of the pyramid is 790.
5)
The answer to number 5 is 2,254.
6)
The last answer is 21.7 centimeters. but I'm not like 100% sure.
The answer is C. Since the sum is less than seven, we need to subtract a fraction. -6 over three is -2. 7-2 is five
We need to determine the radius and diameter of the circle. If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,
A = 10 pi in^2 = pi*r^2. Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.
Thus, the diam. of the circle is 2sqrt(10) in. This diam. has the same length as does the hypotenuse of one of the triangles making up the square.
Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square. So, 4(10) in^2 = 2x^2. Then:
40 in^2 = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20). The area of the square is the square of this result:
Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer). Compare that to the 10 pi sq in area of the circle (31.42 in^2).
