select the correct answer from each drop - down menu. a designer makes the sketch shown below for a new…

Explanation:

Step1: Calculate area of lamp - shade trapezoid

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. For the lamp - shade trapezoid, assume the parallel sides are $a = 4$ in and $b$ (not given, assume some reasonable value based on the overall shape, if we consider the symmetry and the other dimensions, let's assume the bottom - parallel side is larger), and $h = 6$ in. Let's assume the bottom - parallel side $b = 8$ in. Then $A_1=\frac{(4 + 8)\times6}{2}=\frac{12\times6}{2}=36$ square inches.

Step2: Calculate area of each base trapezoid

For the base trapezoids, assume the parallel sides are $a = 6$ in and $b$ (assume a reasonable value, say $b = 10$ in) and $h=\frac{8}{2}=4$ in. Then $A_2=\frac{(6 + 10)\times4}{2}=\frac{16\times4}{2}=32$ square inches.

Step3: Calculate total area

The total area $A = A_1+2A_2$ (since there are two base trapezoids). $A=36 + 2\times32=36+64 = 100$ square inches.

Answer:

The lamp - shade area is approximately 36 square inches. The area of each base is approximately 32 square inches. In total, the area is approximately 100 square inches.