# Find the lateral and total surface area of the following pyramids.

(a) Square-based pyramid with base 6cm and slant height 14 cm.

(b) Triangular-based pyramid with base 12cm and slant height 20cm.

**Solution:**

Given,

(a) Square-based pyramid with base 6cm and slant height 14 cm.

Perimeter of the base = perimeter of the square base = P

P = 4 × side = 4 × 6 = 24 cm

Lateral surface area of the pyramid = 1/2 P l

where, l = slant height

LSA = 1/2 × 24 × 14 = 168 cm^{2}

Total area of the base = Lateral surface area + Area of the base

TSA = LSA + Area

Area of the square based pyramid = side^{2}

Area of the base = 62 = 36 cm^{2}

**∴ TSA = 168 + 36 = 204 cm ^{2}**

(b) Triangular-based pyramid with base 12cm and slant height 20cm.

Perimeter of the base = perimeter of the square base = P

P = 3 × side = 3× 12 = 36 cm

Lateral surface area of the pyramid = 1/2 P l

where, l = slant height

LSA = 1/2 × 36 × 20 = 360 cm^{2}

Total area of the base = Lateral surface area + Area of the base

TSA = LSA + Area

Area of the triangular pyramid = √3/4 s^{2}

Area of the base = √3/4 ×(12)^{2} = √3/4 × 144 = 36√3 cm^{2}

**∴ TSA = 360 + 36√3 = 36(10 + √3) cm ^{2}**

## Find the lateral and total surface area of the following pyramids.

(a) Square-based pyramid with base 6cm and slant height 14 cm.

(b) Triangular-based pyramid with base 12cm and slant height 20cm.

**Summary: **

(a) The lateral and total surface area of the square-based pyramid with base 6cm and slant height 14 cm are 168 cm2 and 204 cm^{2} respectively.

(b) The lateral and total surface area of the triangular-based pyramid with base 12cm and slant height 20cm are 360 cm2 and 36(10 + √3) cm^{2} respectively.

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