2. Surface Area & Volume of Prisms Tutorial 5c

3. Lateral and Surface Areas of Prisms §The lateral area of a prism is the sum of the areas of the lateral faces. Perimeter of base a + b + c + d = p acbd h Lateral Area = ph h c b a d acbd h base Surface Area = L.A. + 2B Lateral area +Area of base §The surface area is the sum of areas of the lateral faces and the two bases.

4. Lateral and Surface Area Theorem §The lateral area of a right prism is the product of the perimeter of the base and the height. L.A. = ph §The surface area of a right prism is the sum of the lateral area and the areas of the two bases. S.A. = L.A. + 2B = ph + 2B h B is the area of the base. P is the perimeter of a base

5. Example 1: Find the Surface Area Rectangular Prism 30 ft 40 ft 60 ft p = 30 + 40 + 30 + 40 p = 140 h = 60 B= 30 40 B= 1200 S.A. = ph + 2B S.A. = 14060 + 21200 = 8400 + 2400 = 10,800 S.A. = 10,800 ft 2

6. Volume of Prisms §Volume is the space a figure occupies. §It is measured in cubic units such as cubic inches (in 3 ), cubic feet (ft 3 ), or cubic centimeters (cm 3 ). §The volume of a cube is the cube of the length of its edge, V = e 3

7. Volume of a Prism §The volume of a prism is the product of the area of a base and the height of the prism. B h

8. Volume of a Rectangular Prism §The volume of a prism is the product of the area of a base and the height of the prism. §However, to find the area of the base of a rectangular prism you simply multiple the length by the width. §Thus its volume is the length x width x height. Rectangular Prism

9. Example 2: Rectangular Prism 30 ft 40 ft 60 ft V = 120060 = 72,000 B= l w B= 40 30 B= 1200 h = 60 V = Bh V = 72,000 ft 3

10. Example 3: 6 15 B = ½ap 3 a = 5.2 p = 36 To find the area of a Regular Hexagon you would multiply one-half the apothem(a) by the perimeter of the base(p). ( 1 / 2 ap)