Answer:
correct answer is 456 sq units.
Step-by-step explanation:
Let us have a look at the formula for Surface Area of a prism:
[tex]A =p \times h+2 \times B[/tex]
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
[tex]20^2=12^2+side^2\\\Rightarrow 400=144+side^2\\\Rightarrow side =\sqrt{256}\\\Rightarrow side =16\ units[/tex]
Area of base = area of right angled triangle:
[tex]B = \dfrac{1}{2} \times \text{Base Length} \times \text{Perpendicular Length}\\\Rightarrow B = \dfrac{1}{2} \times 16\times 12 = 96\ sq\ units[/tex]
Perimeter [tex]\times[/tex] height = (12+20+16) [tex]\times[/tex] 7.5 = (48) [tex]\times[/tex] 7.5 = 360 sq units
Now putting the values in formula:
Surface area, A = 360+96 = 456 sq units
So, correct answer is 456 sq units.
