The area of all the faces of the stage, excluding the bottom is: 292 ft²
How to find the surface area?
To find the surface of all the faces of the stage excluding the base, we will find each individual area and add up together.
The formula for the area of a trapezium is given by the formula:
A = ¹/₂(sum of parallel sides) * height
Thus:
A = ¹/₂(20 + 10) * 12
A = 180 ft²
Area of the remaining faces = 2(13 * 2) + (10 * 2) + (20 * 2) = 112 ft²
Total surface area = 180 ft² + 112 ft²
Total surface area = 292 ft²
Complete question is:
A drama club is building a wooden stage in the shape of a trapezoidal prism. The height of the stage is 2 feet. Some measurements of the stage are shown here. What is the area of all the faces of the stage, excluding the bottom?