Explanation:
First, find the area of the lampshade.
The lampshade is in the shape of a trapezoid; the area of a trapezoid is calculated using the formula:
[tex]\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}[/tex]
Thus, the area of the lampshade is approximately:
[tex]A=\frac{1}{2}(7+4)6=11\times3=33\approx30\; in.^2[/tex]
Next, we find the area of the base.
The base is made up of two trapezoids and the area of one of the trapezoids is approximately:
[tex]A=\frac{1}{2}(3+6)\times\frac{8}{2}=\frac{1}{2}\times9\times4=18\; in\text{.}^2[/tex]
Thus, the total area is approximately:
[tex]\text{Total Area}=30+2(18)=30+36\approx66\; in\text{.}^2[/tex]
Therefore:
Answer:
• The lampshade is a trapezoid. Its area is approximately ,30 square inches.
,
• The bases of the lamp are two trapezoids. The area of each is approximately ,18 square inches,.
,
• In total, the area is approximately ,66 square inches,.
