A gift box is in the shape of a trapezoidal prism with base lengths of7 inches and 5 inches and a height of 4 inches. The height of the gift box is 8 inches. What is the volume of the gift box?

192 in³

Step-by-step explanation:

A trapezoidal prism is a three dimensional solid that has two similar trapezoids at its top and base. The two similar trapezoids are connected by four rectangles connecting the corresponding sides of the two bases.

The Area of the trapezoid at the top or base = 1/2 (a + b) h

Where a and b are the lengths = 7 inches and 5 inches and the height (h) = 4 inches.

Therefore Area of the trapezoid at the top or base = 1/2 (a + b) h = 1/2 (7 + 5) 4 = 24 in²

The volume of gift box = Area of the trapezoid at the top or base * height of gift box = 24 * 8 = 192 in³