1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.3 Area

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Understand the concept of area. o Know the formulas for finding the area of five polygons.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Formulas for Area Notes In triangles and other figures, we have used the letter h to represent the height of the figure. The height is also called the altitude and is perpendicular to the base.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Formulas for Area Formulas for the Area of Five Polygons

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Area of a Triangle Find the area of a triangle with height 4 in. and base 10 in.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Area of a Triangle (cont.) Solution To find the area of a triangle, multiply by the base and the height. (Be sure to label the answer in square inches.) The area of the triangle is 20 in. 2

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Area of a Trapezoid Find the area of a trapezoid with altitude 6 in. and parallel sides of length 12 in. and 24 in. Solution First draw a figure and label the lengths of the known parts.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Area of a Trapezoid (cont.) The area of the trapezoid is 108 in. 2

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Area of a Composite Figure Find the area of the figure shown here with the indicated dimensions. Solution To find the area of this figure, find the area of each part and then add the three areas. The figure is made up of two triangles and one rectangle.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Area of a Composite Figure (cont.) RectangleLarger TriangleSmaller Triangle

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Area of a Rectangle A square is cut out of a rectangle as shown. Find the area of the orange shaded region. Solution There are three steps in finding the area of the shaded region. Find the area of the outer figure. Find the area of the inner figure. Find the difference between the areas.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Area of a Rectangle (cont.) Step 1:Find the area of the rectangle. Step 2:Find the area of the square. Step 3:Find the difference between the two areas. The area of the shaded region is 650 ft 2.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Area of a Polygon The polygon shown here is a rectangle with a rectangular piece missing. Find the area of the polygon. Solution There are several ways of finding the area of this figure. One way is to find the area of each of the three parts as illustrated here and then adding the three areas.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Area of a Polygon (cont.)

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Perimeter and Area A baseball infield is in the shape of a square 90 feet on each side. a.What is the perimeter of the infield? b.What is the area of the infield?

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Perimeter and Area (cont.) Solutions a. b. The perimeter of the infield is 360 feet and the area is 8100 square feet.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Find the area of each polygon. 1.2.

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) 3.Find the area of a parallelogram with base 1.6 m and height 2.4 m. 4.A rectangle is 40 meters wide and 90 meters long (a soccer field). Find a. the perimeter of the rectangle and b. the area of the rectangle.

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers