find the surface area of the composite figure. sa = ? in² remember! exclude areas where complex shapes touch.
find the surface area of the composite figure. sa = ? in² remember! exclude areas where complex shapes touch.
Answer
Explanation:
Step1: Calculate surface - area of pink prism
The surface - area formula for a rectangular prism is $SA = 2(lw+lh+wh)$. For the pink prism with $l = 2$, $w = 2$, $h = 10$, the surface - area $SA_1=2(2\times2 + 2\times10+2\times10)=2(4 + 20 + 20)=2\times44 = 88$ square inches. But we need to exclude the area of the touching face. The area of the touching face is $2\times4 = 8$ square inches. So the net surface - area of the pink prism is $SA_{1net}=88-8=80$ square inches.
Step2: Calculate surface - area of green prism
For the green prism with $l = 4$, $w = 4$, $h = 7$, the surface - area formula gives $SA_2=2(4\times4+4\times7 + 4\times7)=2(16+28 + 28)=2\times72=144$ square inches. We also need to exclude the area of the touching face ($2\times4 = 8$ square inches). So the net surface - area of the green prism is $SA_{2net}=144 - 8=136$ square inches.
Step3: Calculate total surface - area
The total surface - area of the composite figure $SA=SA_{1net}+SA_{2net}=80 + 136=216$ square inches.
Answer:
216