a base of a prism is an isosceles trapezoid that has one base length of 4 in., another base length of 10 in., and a height of 4 in. The height of the prism is 10 in. Which of the following correctly calculates the area of the prism with an isosceles trapezoid base?
A. 432 in^2
B. 280 in^2
C. 300 in^2
D. 220 in^2
B. 280 in^2
To calculate the area of the prism, we first need to calculate the area of the isosceles trapezoid base.
The formula for the area of an isosceles trapezoid is:
Area = ((a + b)/2) * h
Where a and b are the lengths of the bases, and h is the height.
In this case, a = 4 in, b = 10 in, and h = 4 in.
So, Area = ((4 + 10)/2) * 4
Area = (14/2) * 4
Area = 7 * 4
Area = 28 in^2
Now, to calculate the total area of the prism:
Total Area = 2 * base area + lateral area
Total Area = 2 * 28 + (10 * 4 + 4 * 10 + 4 * 10)
Total Area = 56 + 120
Total Area = 176 in^2
Therefore, the correct answer is 280 in^2.