5-Minute Check on Lesson 11-35-Minute Check on Lesson 11-35-Minute Check on Lesson 11-35-Minute Check on Lesson 11-3 Transparency 11-4

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Find the area of each regular polygon. Round to the nearest tenth if necessary.

1. A hexagon with side length 8 cm.

2. A square with an apothem length of 14 in.

3. A triangle with a side length of 18.6 m.

Find the area of each shaded region. Assume all polygons are regular. Round to the nearest tenth if necessary.

4. 5.

6. Find the area of a circle with a diameter of 8 inches.Standardized Test Practice:

A CB D4π 8π 16π 64π

A = 784 in²

A = 92.5 units²

C

A = 166.3 cm²

A = 149.8 m²

A = 51.4 units² 9

5

Lesson 11-4

Areas of Irregular Figures

Objectives

• Find areas of irregular figures

• Find areas of irregular figures on the coordinate plane

Area of Irregular Shapes

Irregular Shapes Area: Sum of Separate Parts

x

r

h

Example Area: A = ½ circle + triangle + squareA = ½ * πr2 + ½ x * h + x * x

Irregular Shapes Example 112

6 812

Area of shape = Area of semi-circle + Area of square + Area of triangle

semi-circle area = ½ πr² = ½ π6² = 18π

square area = s² = 12² = 144

triangle area = ½ bh = ½ 12(8) = 48

Area of shape = 18π + 144 + 48 = 192 + 18π = 248.55

Irregular Shapes Example 2120 yards

30 yds 812

Area of shape = 2 Areas of semi-circle + Area of rectangle

2*semi-circle area = 2(½ πr²) = π30² = 900π

rectangle area = l·w = 120·60 = 7200

Area of shape = 900π + 7200 = 10,027.43 square yards

Find the area of the figure in square feet. Round to the nearest tenth if necessary.

The figure can be separated into a rectangle with dimensions 16 feet by 32 feet, a triangle with a base of 32 feet and a height of 15 feet, and two semicircles with radii of 8 feet.

Answer: The area of the irregular figure is 953.1 square feet to the nearest tenth.

Substitution

Simplify.

Area formulas

Use a calculator.

Answer:

Find the area of the figure in square feet. Round to the nearest tenth if necessary.

A rectangular rose garden is centered in a border of lawn. Find the area of the lawn around the garden in square feet.

The length of the entire lawn is 25 + 100 + 25 or 150 feet. The width of the entire lawn is 25 + 20 + 25 or 70 feet. The length of the rose garden is 100 feet and the width is 20 feet.

rose garden

Answer: The area of the lawn around the garden is 8500 sq feet.

Simplify.

Substitution

Simplify.

Area formulas

area of irregular figure = area of entire lawn – area of rose garden

INTERIOR DESIGN Cara wants to wallpaper one wall of her family room. She has a fireplace in the center of the wall. Find the area of the wall around the fireplace.

Answer:

Find the area of polygon MNPQR.

First, separate the figure into regions. Draw an auxiliary line perpendicular to QR from M (we will call this point S) and an auxiliary line from N to the x-axis (we will call this point K).

This divides the figure into triangle MRS, triangle NKM, trapezoid POKN and trapezoid PQSO.

Find the difference between x-coordinates to find the lengths of the bases of the triangles and the lengths of the bases of the trapezoids.

Now, find the area of each of the figures.

Find the difference between y-coordinates to find the heights of the triangles and trapezoids.

Answer: The area of polygon MNPQR is 44.5 sq units.

Simplify.

Substitution

Area formulas

Find the area of polygon ABCDE.

Answer:

Summary & Homework

• Summary:– The area of an irregular figure is the sum

of the areas of its nonoverlapping parts

• Homework: – pg 619-621; 3, 8-13