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Mensuration is a pure formula-based topic and tricks/shortcuts are seldom applied here. So in this series I will try to solve all the mensuration problems that have appeared in CGL lately and in the process I will share the important concepts/formulas.

__For Prism and Calendar (figures with uniform girth) –__

Lateral Surface Area = Height * Perimeter of the Base

Volume = Height * Area of the Base

In this question the Total surface area is being asked

**Total Surface Area of a Prism = Lateral Surface Area + Area of the two bases**

Height of the prism = 10 cm

Perimeter of the base = 5 + 12 + 13 (Calculate the hypotenuse with Pythagoras Theorem) = 30 cm

So Lateral Surface Area = 10 * 30 = 300 cm

Area of the base = 1/2 * base * height = 1/2 * 5 * 12 = 30 cm

So Total Surface Area = 300 + 2*30 = 360 cm

**Answer : (A)**

^{2 }* h

^{2 }* H = 27 * 1/3 * π * r

^{2 }* h

27 * (r/R)^2=H/h

Put the value of r/R from equation (1)

^{3}= H

^{3}

Put H = 30 cm

**Answer : (B)**

Area of triangle BDC = 84 cm (Apply Heron’s formula)

Area of base/quadrilateral = 84 + 54 = 138 cm

Volume = Height * Area of the Base

2070 = Height * 138

So, Height of the prism = 15 cm

Lateral Surface Area = Height * Perimeter of the Base

Perimeter of the base = AB + BC + CD + DA = 48 cm

Lateral Surface Area = 48 * 15 = 720 cm^2

**Answer : (A)**

Perimeter of the base = 3a

Volume of the prism = Area of the base * Height =√3/4 * a^2 * h … (1)

Lateral surface Area of the prism = Perimeter of the base * Height = 3a * h …(2)

Divide equation (1) by (2)

Volume/Area = (1/4√3) * a

40√3/120 = a/4√3 [Since Volume = 40√3 and Lateral surface Area = 120]
a = 160 * 3/120

**Answer : (A)**

**Slant edge**and

**Slant Height**

**V = 1/3 * A * h**

**Answer : (D)**