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?
To calculate the area of the prism with an isosceles trapezoid base, we first need to find the area of the trapezoid base and then multiply it by the height of the prism.
The formula for the area of a trapezoid is:
Area = 1/2 * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.
Plugging in the values given:
b1 = 4 in.
b2 = 10 in.
h = 4 in.
Area of the trapezoid base = 1/2 * (4 + 10) * 4
Area of the trapezoid base = 1/2 * 14 * 4
Area of the trapezoid base = 28 sq. in.
Now, to find the area of the prism, we need to multiply the area of the trapezoid base by the height of the prism:
Area of the prism = 28 sq. in. * 10 in.
Area of the prism = 280 sq. in.
Therefore, the correct calculation for the area of the prism with an isosceles trapezoid base is 280 sq. in.