Base edge of a square pyramid is 24cm and it's slant height 20.a)what is the height?b)find its volume
Answers
Answer:
896 cm2
Step-by-step explanation:
Total surface area = 896 square centimeters
Volume = 1568 cubic centimeters.
Because the vertical height and slant height form the hypotenuse and one leg of a right triangle you can use the pythagorean theorem to find the apothem. And because this is a square based pyramid, the apothem is 1/2 the side of the square.
The volume will equal 1/3 Bh, where B is the area of the square base and h is the height. Using the the pythagorean theorem , the apothem is 7cm (the square root of [25 squared minus 24 squared]). With an apothem of 7, the side is 14 (2 x 7), so the area of the square base is 196 square centimeters (14 squared). So the volume is 1/3(196)(24) = 1568 cubic centimeters.
The surface area is the square base plus 4 identical triangles. From earlier work the square base is 196 square centimeters, and each triangle has a base of 14, the side of the square base, by a height of 25, the slant height. So each triangle is 1/2(14)(25) = 175 square centimeters. So the four triangles will equal 4 x 175 square centimeters = 700 square centimeters. Now add the area of the square base, 700 + 196 = 896 square centimeters.