Question : The base of a right pyramid is square of side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is:
Option 1: 400 cm2
Option 2: 460 cm2
Option 3: 260 cm2
Option 4: 360 cm2
Correct Answer: 360 cm 2
Solution :
Given: Base = 10 cm
Height = 12 cm
$\therefore$ Slant height $=\sqrt{{\text{height}^2+(\frac{\text{base}}{2})^2}}=\sqrt{12^2+5^2}$ = $\sqrt{144+25}=\sqrt{169} = 13$ cm
Lateral surface area = $\frac{1}{2}$ × perimeter of base × slant height = $\frac{1}{2}$ × 40 × 13 = 260 cm
2
Area of base = 10 × 10 = 100 cm
2
$\therefore$ Total surface area = lateral surface area + area of the base = 260 + 100 = 360 cm
2
Hence, the correct answer is 360 cm
2
.
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