Video Transcript
The given figure represents a trapezoidal wooden frame. Determine the surface area of its front side.
In order to find the surface area of the front side of this frame, we need to take the area of the larger trapezoid and subtract the area of the smaller trapezoid. Here would be the larger trapezoid. And this will be the smaller trapezoid.
The formula for the area of a trapezoid is equal to one-half times the height of the trapezoid times the bases added together. So let’s begin with labelling the large trapezoid. This will be the height of the large trapezoid. So its height must be 5.5 inches. Here would be base one. And here would be base two. It wouldn’t matter which one we call base one and base two.
So base one must be 4.8 inches. And base two must be six inches. So here we have the formula written out, the larger area minus the smaller area. So we just need to plug in. So let’s go ahead and plug in our values for the larger trapezoid. The height was 5.5. And the bases were 4.8 and six.
Now let’s label the pieces of the smaller trapezoid. Here will be the height. So the height must be 4.5 inches. Here is base one. So it’s 3.4 inches. And here is base two, which would be 4.8 inches. So let’s go ahead and plug this is in.
So now that we’ve done so, let’s go ahead and simplify. So we needed to add what was inside these parentheses first. And now we simply need to multiply the numbers in blue, multiply the numbers in pink, and then subtract the pink from the blue. So we have 29.7 minus 18.45, giving us a surface area of 11.25 square inches.
