Respuesta :
Answer:
Option D) 294 sq cm is correct
∴ the surface area of the rectangular pyramid is 294 sq cm
Step-by-step explanation:
First we have to split the net into 4 triangles and 1 rectangle
Given a = 12 cm ,b = 6 cm and d = 13 cm
To find the surface area of the rectangular pyramid:
Now find the area of the rectangle base
[tex]Rectangle base area=b\times a[/tex]
[tex]= 6\times 12[/tex]
= 72 sq. cm
∴ Rectangle base area=72 sq cm
Now to find the area of the triangle on the left
[tex]Left triangle=\frac{1}{2}(b)(d)[/tex]
[tex]=\frac{1}{2}(6)(13)[/tex]
= 39 sq cm
∴ Left triangle=39 sq cm
Since all the triangles are congruent , you will need to multiply by 2 to get the combined area of the triangle on the left and on the right.
Area of left and right triangles= 2(39)
=78 sq cm
∴ Area of left and right triangles=78 sq cm
Find the area of the triangle on the bottom
[tex]Bottom triangle area=\frac{1}{2}(a)(a)[/tex]
[tex]=\frac{1}{2}(12)(12)[/tex]
= 72 sq cm
∴ Bottom triangle area=72 sq cm
Since the bottom of the triangle is congruent to the top triangle, multiply that by 2 to get a combined area of the triangle on the bottom and top
Area of top & bottom triangles=2 (72)
= 144 sq cm
∴ Area of top & bottom triangles= 144 sq cm
Finally add the area of the 4 triangles to the area of the rectangular base we get
=72 + 78 + 144
= 294 sq cm
