find the surface area of the composite figure. sa = ? cm² remember! exclude areas where complex shapes touch.
find the surface area of the composite figure. sa = ? cm² remember! exclude areas where complex shapes touch.
Answer
Explanation:
Step1: Calculate surface - area of green cuboid
The surface - area formula of a cuboid is $2(lw + lh+wh)$. For the green cuboid with $l = 10$ cm, $w = 5$ cm, $h = 4$ cm, $SA_{green}=2(10\times5 + 10\times4+5\times4)=2(50 + 40 + 20)=2\times110 = 220$ $cm^{2}$. But we need to subtract the area of the contact part. The contact part has an area of $2\times2=4$ $cm^{2}$. So the adjusted surface - area of the green cuboid is $220-4 = 216$ $cm^{2}$.
Step2: Calculate surface - area of pink cuboid
For the pink cuboid with $l = 2$ cm, $w = 2$ cm, $h = 6$ cm, the surface - area formula of a cuboid is $2(lw + lh+wh)$. But we subtract the contact area of $4$ $cm^{2}$. $SA_{pink}=2(2\times2+2\times6 + 2\times6)-4=2(4 + 12+12)-4=2\times28-4=56 - 4=52$ $cm^{2}$.
Step3: Calculate total surface - area of composite figure
$SA=SA_{green}+SA_{pink}=216 + 52=268$ $cm^{2}$.
Answer:
268