Answer:
correct answer is <em>456 sq units.</em>
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Step-by-step explanation:
Let us have a look at the formula for Surface Area of a prism:
![A =p \times h+2 \times B](https://tex.z-dn.net/?f=A%20%20%3Dp%20%5Ctimes%20h%2B2%20%5Ctimes%20B)
Where p is the perimeter of base
h is the height of prism
and B is the base area of prism.
Given that:
h = 7.5 units
Hypotenuse of prism's base = 20 units
One of the Other sides = 12 units
Pythagorean theorem can be used to find the 3rd side of right angled base.
Square of hypotenuse = Sum of squares of other two sides
![20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units](https://tex.z-dn.net/?f=20%5E2%3D12%5E2%2Bside%5E2%5C%5C%5CRightarrow%20400%3D144%2Bside%5E2%5C%5C%5CRightarrow%20side%20%3D%5Csqrt%7B256%7D%5C%5C%5CRightarrow%20side%20%3D16%5C%20units)
Area of base = area of right angled triangle:
![B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units](https://tex.z-dn.net/?f=B%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Ctext%7BBase%20Length%7D%20%5Ctimes%20%5Ctext%7BPerpendicular%20Length%7D%5C%5C%5CRightarrow%20B%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%2016%5Ctimes%2012%20%3D%2096%5C%20sq%5C%20units)
Perimeter
height = (12+20+16)
7.5 = (48)
7.5 = 360 sq units
Now putting the values in formula:
Surface area, A = 360+96 = 456 sq units
So, correct answer is <em>456 sq units.</em>