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10-2 Estimating and Finding Area
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem 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 1
10-2 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 1
10-2 Estimating and Finding Area
Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms.
Course 1
10-2 Estimating and Finding Area
Vocabulary
area
Insert Lesson Title Here
Course 1
10-2 Estimating and Finding Area
The area of a figure is the amount of surface it covers. We measure area in square units.
Course 1
10-2 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. 19 + 9 + 2 = 30
The area of the figure is about 30 mi .2
Course 1
10-2 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. 11 + 5 + 2 = 18
The area of the figure is about 18 mi .2
= mi2
Course 1
10-2 Estimating and Finding Area
Course 1
10-2 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 in2.
15 in.
9 in.
Course 1
10-2 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 in2.
13 in.
7 in.
Course 1
10-2 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 1
10-2 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 ft12
A = 2 • 112__ 1
4__ Substitute 2 for b
and 1 for h.
12__
14__
A = •52__ 5
4__
A = or 325 8
___ 18__
The area is 3 ft2. 18__
14
1 ft
Course 1
10-2 Estimating and Finding Area
Try This: Example 3
Find the area of the parallelogram.
Write the formula.
Multiply.
A = bh
A = 1 • 312__ 1
2__ Substitute 1 for b
and 3 for h.
12__
12__
A = •32__ 7
2__
A = or 521 4
___ 14__
The area is 5 ft2.14__
11 ft2
13 ft2
Course 1
10-2 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.12__
Course 1
10-2 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 13.92 cm2.
A = 13.92
A = bh12__
A = (9.6 • 2.9)12__
A = (27.84)12__
Course 1
10-2 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 14.45 cm2.
3.4 cm
8.5 cm
A = 14.45
A = bh12__
A = (8.5 • 3.4)12__
A = (28.9)12__
Course 1
10-2 Estimating and Finding Area
Lesson Quiz
Find the area of each figure.
1. 2.
3. 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 m41.4 m2 24 ft2
160 in2
35 in2
Course 1
10-2 Estimating and Finding Area