Explanation Formula used: The lateral surface area of a pyramid is given by L = 1 2 P s , where P is the perimeter of the base and s is the slant height of the lateral face. The total surface area is calculated using the formula S = L + A where L is the lateral surface area and A is the area. The volume of a pyramid is given by the formula V = 1 3 h A , where A is the area and h is the altitude of the base. Calculation: From the given figure, it is to be noted that the s = 20 cm and h = 10 cm . Observe that, the base of the given pyramid is a regular hexagon with side a = 20 cm . Obtain the perimeter of the regular hexagon of side a = 20 cm as shown below: Perimeter, P = 6 a = 6 ( 20 cm ) = 120 cm That is, the perimeter of the regular hexagon is 120 cm. Substitute the values s = 20 cm , P = 120 cm in the formula L = 1 2 P s and obtain the lateral surface area of the pyramid as shown below: L = 1 2 P s = 1 2 ⋅ ( 120 cm ) ⋅ ( 20 cm ) = 1200 sq cm Thus, the lateral surface area of the pyramid is 1200 sq cm

10th Edition

ISBN: 8220100803055

Author: SAUNDERS

Publisher: PEARSON

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Question

Chapter 9.2, Problem 8BE

To determine

The total outside surface area and volume of the given pyramid and to round the result to three significant digits.

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Chapter 9.2, Problem 7BE

Chapter 9.2, Problem 1CE

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Proof: LN⎯⎯⎯⎯⎯LN¯ divides quadrilateral KLMN into two triangles. The sum of the angle measures in each triangle is ˚, so the sum of the angle measures for both triangles is ˚. So, m∠K+m∠L+m∠M+m∠N=m∠K+m∠L+m∠M+m∠N=˚. Because ∠K≅∠M∠K≅∠M and ∠N≅∠L, m∠K=m∠M∠N≅∠L, m∠K=m∠M and m∠N=m∠Lm∠N=m∠L by the definition of congruence. By the Substitution Property of Equality, m∠K+m∠L+m∠K+m∠L=m∠K+m∠L+m∠K+m∠L=°,°, so (m∠K)+ m∠K+ (m∠L)= m∠L= ˚. Dividing each side by gives m∠K+m∠L=m∠K+m∠L= °.°. The consecutive angles are supplementary, so KN⎯⎯⎯⎯⎯⎯∥LM⎯⎯⎯⎯⎯⎯KN¯∥LM¯ by the Converse of the Consecutive Interior Angles Theorem. Likewise, (m∠K)+m∠K+ (m∠N)=m∠N= ˚, or m∠K+m∠N=m∠K+m∠N= ˚. So these consecutive angles are supplementary and KL⎯⎯⎯⎯⎯∥NM⎯⎯⎯⎯⎯⎯KL¯∥NM¯ by the Converse of the Consecutive Interior Angles Theorem. Opposite sides are parallel, so quadrilateral KLMN is a parallelogram.

Chapter 9 Solutions

EBK MATHEMATICS FOR THE TRADES

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