How do i find the surface area of this figuere?

Question

anonymous · Answer

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anonymous · Answer

From the top and bottom views, you are looking at squares. The smaller square has sides that equal 4cm, the larger square has sides that equal 6cm. Then you have 4 trapezoids with $base_1 = 4$ and $base_2 = 6$ and a height of 5.

The surface area of this figure is simply the area of each of these shapes combined. The formula will look like this:
$$surface~area = area(top) + area(bottom) + 4(area(trapezoid))$$
The area of a square is $side^2$ and the area of a trapezoid is $\frac{1}{2}h(b_1+b_2)$
$$sa = 4^2 + 6^2 + 4(\frac{1}{2}(5)(4+6))$$
The rest is just arithmetic:
$$sa = 16 + 36 + 4(\frac{1}{2}(5)(10)$$
$$sa = 52 + 4(\frac{1}{2}(50))$$
$$sa = 52 + 4(25)$$
$$sa = 52 + 100$$
$$sa = 152$$