Question : The total surface area of a right pyramid on a square base of side 10 cm with height 12 cm is:
Option 1: 260 cm2
Option 2: 360 cm2
Option 3: 330 cm2
Option 4: 300 cm2
Correct Answer: 360 cm 2
Solution :
In $\triangle$OAB,
Slant height, $l$ = $\sqrt {h^2 + AB^2}$
= $\sqrt {12^2 + 5^2}$
= $\sqrt{169}$
= $13$ cm
Total surface area = lateral surface area + area of the base
= $\frac{1}{2}$ × perimeter of base × slant height + area of the base
= $\frac{1}{2} × (4 × 10) × 13 + 10^2$
= $260+100$
= $360$ cm
2
Hence, the correct answer is 360 cm
2
.
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