Question

A right prism of height 14 inches has a base made of a rhombus whose diagonals are 6

inches and 8 inches long.

Answer 1

(a)24 square inches

(b)280 Square Inches.

(c)192 cubic inches

Explanation:

(a)Given the diagonals of a rhombus:

Area=½ X Product of the diagonals

Therefore:

Area=½ X 6 X 8

Base Area=24 square inches

(b)Lateral Area

Lateral Area of a Prism=Base Perimeter X Height

Applying Pythagorean Triples(3,4,5) in the attached triangle

Side Length=5 inches

Base Perimeter=4*5=20 Inches

Lateral Area =20*14=280 Square Inches.

(c)Volume

Volume of a Prism=Base Area X Height

=24*8

Volume=192 cubic inches