Craig has a building block in the shape of a rectangular pyramid. a net of which is shown below.

if a measures 12 cm, b measures 6 cm, and d measures 13 cm, what is the surface area of the rectangular pyramid?
a. 183 sq cm
b. 936 sq cm
c. 516 sq cm
d. 294 sq cm

the answer is D: 294 sq. cm

Step-by-step explanation:

first you want to split the net into 4 triangles and 1 rectangle

a = 12 cm

b =  6 cm

d = 13 cm

calculate the surface area of the pyramid...

1st find the area of the rectangle base

Rectangle base area

b x a = (6 cm) (12 cm)

= 72 sq. cm

next find the area of the triangle on the left

Left triangle

1/2(b)(d) = 1/2 (6 cm)(13 cm)

= 1/2 (78 sq cm)

= 39 sq. cm

Since all the triangles are congruent (same), 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 & right triangles

= 2 (39 sq. cm)

= 78 sq. cm

Find the area of the triangle on the bottom

Bottom triangle area = 1/2 (a)(a)

= 1/2 (12 cm) (12 cm)

= 1/2 (144 sq. cm)

= 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 sq. cm) = 144 sq. cm

Finally...add the area of the 4 triangles to the area of the rectangular base

72 + 78 + 144 = 294 sq. cm

20

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25

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