1. Area of Squares and Rectangles Section 8.3

2. Goal Find the area of squares and rectangles.

3. Key Vocabulary Area Square Rectangle

4. Definition: Area Area is the amount of space inside a figure. We use square units to describe area.

5. What Is Area ? Area is the amount of space inside a shape: Area Area is measured in square units. 1unit A square unit is a square measuring one unit in each direction. It is written as: 1unit 2

6. The area of a closed figure is the number of square units contained in the figure. 4 units 2 units Area of Rectangles and Squares

7. What is the area of the rectangle? In other words, how many unit squares are contained within the rectangle?

8. Area of Rectangles and Squares Notice that finding the area of a rectangle is exactly the same as using a multiplication table. 123456789101112131415 1123456789101112131415 224681012141618202224262830 3369121518212427303336394245 44812162024283236404448525660 551015202530354045505560657075 661218243036424854606672788490 7714212835424956637077849198105

9. Area of Rectangles and Squares base height Any one of the sides of a rectangle can be considered a base. A rectangle’s height is the length of the side that is perpendicular to the base. Bases and Heights

10. Area of a Rectangle The area of a rectangle is the product of its base and height. Words: Area = (base)(height) Symbols: A = bh

11. Area of a Square For squares, the formula is still A=bh. However, since every side of a square is the same, then it can also be expressed as A=s 2 where s equals the length of one side. Words: Area = (side) 2 Symbols: A = s 2

12. Find the Area of a Square Example 1 Find the area of the square. SOLUTION Use the formula for the area of a square and substitute 9 for s. A = s 2 Formula for the area of a square = 92= 92 Substitute 9 for s. = 81 Simplify. The area of the square is 81 square feet. ANSWER

13. Find the Area of a Rectangle Example 2 Find the area of the rectangular pool. Use the formula for the area of a rectangle. Substitute 24 for b and 16 for h. SOLUTION A = bh Formula for the area of a rectangle = 24 · 16 Substitute 24 for b and 16 for h. = 384 Multiply. The area of the pool is 384 square feet. ANSWER

14. Find the Height of a Rectangle Example 3 Use the formula for the area of a rectangle and substitute 54 for A and 9 for b. SOLUTION A = bh Formula for the area of a rectangle 54 = 9h Substitute 54 for A and 9 for b. 6 = h Divide each side by 9. The height of the rectangle is 6 inches. ANSWER The rectangle has an area of 54 square inches. Find its height.

15. Your Turn: Find the area of the quadrilateral. 1. 2. 3. A rectangle has an area of 52 square meters and a height of 4 meters. Find the length of its base. 4. ANSWER 121 m 2 ANSWER 12 ft 2 ANSWER 26.55 yd 2 ANSWER 13 m

16. Find the area of this figure. All angles are right angles. Dimensions are in centimeters. Use formulas. 5 2 2 4 A2A2 A1A1 Dividing Complex Polygons into Rectangles

17. Find the area of the shaded portion of this figure. All angles are right angles. Dimensions are in meters. Use formulas. 6 2 10 8A2A2 A1A1 Dividing Complex Polygons into Rectangles

18. Divide a Complex Polygon into Rectangles Example 4 Rectangle B The height is 7 units. The base of rectangle B is the total of both bases minus the base of rectangle A, or 9 – 5 = 4 units. Find the dimensions of rectangles A and B. SOLUTION Rectangle A The base is 5 units. Because rectangle B is 2 units taller than rectangle A, the height of rectangle A is 7 – 2 = 5 units.

19. Find the Area of a Complex Polygon Example 5 SOLUTION Add the areas of the rectangles. Area = Area of F + Area of G + Area of H = bh + bh + bh = 4 · 3 + (7 – 4) · (9 – 2) + 5 · 2 = 4 · 3 + 3 · 7 + 5 · 2 = 12 + 21 + 10 = 43 The total area of the polygon is 43 square centimeters. ANSWER Find the area of the polygon made up of rectangles.

20. Your Turn: Find the area of the polygon made up of rectangles. 1. 2. ANSWER 30 in. 2 ANSWER 54 m 2

21. Assignment: Pg. 427 – 429: # 1 – 9 all, 11 – 29 odd