Question

an 8 inch by 6 inch rectangle is the base of the rectangular prism below. what is the lateral area of the figure? 140 square inches 140 inches 236 square inches 236 inches

Explanation:

Step1: Identify lateral - face dimensions

The lateral faces of a rectangular prism with base dimensions 8 in by 6 in and height 5 in are two pairs of rectangles. One pair has dimensions 8 in by 5 in and the other has dimensions 6 in by 5 in.

Step2: Calculate area of first - type lateral faces

The area of a rectangle is $A = l\times w$. For the rectangles with dimensions 8 in by 5 in, the area of one such rectangle is $A_1=8\times5 = 40$ square inches. Since there are 2 such rectangles, their combined area is $2\times40=80$ square inches.

Step3: Calculate area of second - type lateral faces

For the rectangles with dimensions 6 in by 5 in, the area of one such rectangle is $A_2 = 6\times5=30$ square inches. Since there are 2 such rectangles, their combined area is $2\times30 = 60$ square inches.

Step4: Calculate total lateral area

The total lateral area $A_{lateral}=80 + 60=140$ square inches.

Answer:

140 square inches