10-2 Estimating and Finding Area Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up 1. What is the perimeter of a square with side lengths of 15 in.? 2. What is the perimeter of a rectangle with length 16 cm and width 11 cm? 60 in. 54 cm Course Estimating and Finding Area

Problem of the Day Two wibbles equal four wabbles, and eight wabbles equal two bibbles. If a square has a perimeter of 16 wibbles, what is its area in square bibbles? 4 square bibbles Course Estimating and Finding Area

Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms. Course Estimating and Finding Area

Vocabulary area Insert Lesson Title Here Course Estimating and Finding Area

The area of a figure is the amount of surface it covers. We measure area in square units. Course Estimating and Finding Area

Additional Example 1: Finding the Area of an Irregular Figure Find the area of the rectangle. Count full squares: 19 red squares. Count almost-full squares: 9 blue squares. Count squares that are about half- full: 4 green squares = 2 full squares. Do not count almost empty yellow squares. Add = 30 The area of the figure is about 30 mi. 2 Course Estimating and Finding Area

Try This: Example 1 Estimate the are of the figure. Count full squares: 11 red squares. Count almost-full squares: 5 green squares. Count squares that are about half- full: 4 blue squares = 2 full squares. Do not count almost empty yellow squares. Add = 18 The area of the figure is about 18 mi. 2 = mi 2 Course Estimating and Finding Area

Course Estimating and Finding Area

Additional Example 2: Estimating the Area of a Rectangle Find the area of the figure. Write the formula. Substitute 15 for l. Substitute 9 for w. A = lw A = 15 9 A = 135 The area is about 135 in in. 9 in. Course Estimating and Finding Area

Try This: Example 2 Find the area of the figure. Write the formula. Substitute 13 for l. Substitute 7 for w. A = lw A = 13 7 A = 91 The area is about 91 in in. 7 in. Course Estimating and Finding Area

You can use the formula for the area of a rectangle to write a formula for the area of a parallelogram. Imagine cutting off the triangle drawn in the parallelogram and sliding it to the right to form a rectangle. The area of a parallelogram = bh. The area of a rectangle = lw. The base of the parallelogram is the length of the rectangle. The height of the parallelogram is the width of the rectangle. Course Estimating and Finding Area

Additional Example 3: Finding the Area of a Parallelogram Find the area of the parallelogram. Write the formula. Multiply. A = bh 2 ft 1 2 A = __ 1 4 Substitute 2 for b and 1 for h. 1 2 __ 1 4 A = 5 2 __ 5 4 A = or ___ 1 8 __ The area is 3 ft __ ft Course Estimating and Finding Area

Try This: Example 3 Find the area of the parallelogram. Write the formula. Multiply. A = bh A = __ 1 2 Substitute 1 for b and 3 for h. 1 2 __ 1 2 A = 3 2 __ 7 2 A = or ___ 1 4 __ The area is 5 ft __ 1 1 ft ft 2 Course Estimating and Finding Area

You can make a parallelogram out of two congruent triangles. The area of each triangle is half the area of the parallelogram, so the formula for the area of a triangle is A = bh. 1 2 __ Course Estimating and Finding Area

Additional Example 4: Finding the Area of a Triangle Find the area of the triangle. Write the formula. Substitute 9.6 for b. Substitute 2.9 for h. Multiply. The area is cm 2.A = A = bh 1 2 __ A = ( ) 1 2 __ A = (27.84) 1 2 __ Course Estimating and Finding Area

Try This: Example 4 Find the area of the triangle. Write the formula. Substitute 8.5 for b. Substitute 3.4 for h. Multiply. The area is cm cm 8.5 cm A = A = bh 1 2 __ A = ( ) 1 2 __ A = (28.9) 1 2 __ Course Estimating and Finding Area

Lesson Quiz Find the area of each figure What is the area of a parallelogram with base 16 in. and height 10 in.? 4. What is the area of a triangle with base 10 in. and height 7 in.? Insert Lesson Title Here 4.5 m 9.2 m 41.4 m 2 24 ft in 2 35 in 2 Course Estimating and Finding Area