Question

A pyramidal roof is designed as part of a museum aesthetics, given the
dimensions 10 ft. height and 17 ft. base edge, what is the lateral surface area of
the roof?

Answer 1

Given:

A pyramidal roof is designed as part of a museum aesthetics, given the

dimensions 10 ft. height and 17 ft. base edge

To find:

The lateral surface area of  the roof

Solution:

The height of the square-based pyramid, h = 10 ft

The base edge of the square-based pyramid, a = 17 ft

∴ Slant height "l" of the square-based pyramid is,

= $\sqrt{h^2 + (\frac{a}{2})^2 }$

substituting the values

= $\sqrt{10^2 + (\frac{17}{2})^2 }$

= $\sqrt{100 + 72.25}$

= $\sqrt{172.25}$

= $13.1244\:ft$

Now,

The lateral surface area of the pyramidal roof is,

= 4 × Area of 4 triangular faces

= 4 × ½ × base × slant height

= 2 × a × l

substituting the values of a & l, we get

= 2 × 17 × 13.1244

= 446.22 ft²

Thus, the lateral surface area of  the pyramidal roof is → 446.22 ft².

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Also View:

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

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

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