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  • 3 years ago

How do i find the surface area of this figuere?

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  1. anonymous
    • 3 years ago
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  2. anonymous
    • 2 years ago
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    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: \[sa = 16 + 36 + 4(\frac{1}{2}(5)(10)\] \[sa = 52 + 4(\frac{1}{2}(50))\] \[sa = 52 + 4(25)\] \[sa = 52 + 100\] \[sa = 152\]

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