Ch 10.5

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

Trapezoid LMNO has an area of 55 square units. Find the height.

Find the height of a trapezoid that has an area of 64 square inches, and bases of 8 and 12 inches.

5 (10 + 18) = 70 2

55 = h (8 + 14) h = 5 2

64 = h (8 + 12) h = 6.4 cm 2

Ch 10.5Areas of Regular Polygons

Standard 10.0Students compute areas of polygons.

Learning Target:I will be able to find the areas of regular polygons.

Ch 10.5Ch 10.5

Ch 10.5

Area of a Regular Polygon

FURNITURE The top of the table shown is a regular hexagon with a side length of 3 feet and an apothem of 1.7 feet. What is the area of the tabletop to the nearest tenth?

Step 1 Since the polygon has 6 sides, the polygoncan be divided into 6 congruent isoscelestriangles, each with a base of 3 ft and aheight of 1.7 ft.

Ch 10.5

Area of a Regular Polygon

Step 2 Find the area of one triangle.

Area of a triangle

b = 3 and h = 1.7

Simplify.

Step 3 Multiply the area of one triangle by the totalnumber of triangles.

= 2.55 ft2

Since there are 6 triangles, the area of the table is 2.55 ● 6 or 15.3 ft2.

A. 6 ft2

B. 7 ft2

C. 8 ft2

D. 9 ft2

UMBRELLA The top of an umbrella shown is a regular hexagon with a side length of 2 feet and an apothem of 1.5 feet. What is the area of the entire umbrella to the nearest tenth?

Ch 10.5

center of a regular polygon

a point in the interior that is equidistant from all the vertices.

apothem

a segment drawn from the center that is perpendicular to a side of the regular polygon.

Note: In any regular polygon, all apothems are congruent.

Ch 10.5

Identify Center and Apothem in Regular Polygons

In the figure, pentagon PQRST is inscribed in Identify the center and apothem of the polygon.

center:

apothem:

Ch 10.5

point X

XN

Ch 10.5

Theorem 10-5

Use the Formula for the Area of a Regular Polygon

A. Find the area of the regular hexagon with a side length of 5 meters and an apothem of 2.5√3 meters.

Ch 10.5

Area of a regular polygon

≈ 65.0 m2 Use a calculator.

2.5√3 m

A. 73.1 m2

B. 96.5 m2

C. 126.8 m2

D. 146.3 m2

A. Find the area of the regular hexagon with sides of 7.5 m and apothem of 6.5 m. Round to the nearest tenth.

Ch 10.5

Use the Formula for the Area of a Regular Polygon

B. Find the area of the regular pentagon with a side length of 10.58 cm and an apothem of 7.28 cm. Round to the nearest tenth.

Ch 10.5

Area of a regular polygon

Use a calculator.

€

=1

27.28( ) 5 10.58( )[ ]

A. 113.8 m2

B. 124.5 m2

C. 138.9 m2

D. 143.1 m2

B. Find the area of the regular pentagon with a side length of 7 m and an apothem of 6.5 m. Round to the nearest tenth.

Ch 10.5

Find the area of the shaded figure.

To find the area of the figure, subtract the area of the smaller rectangle from the area of the larger rectangle. The length of the larger rectangle is 25 + 100 + 25 or 150 feet. The width of the larger rectangle is 25 + 20 + 25 or 70 feet.

Ch 10.5

Find the Area of a Composite Figure by Subtracting

Ch 10.5

Find the Area of a Composite Figure by Subtracting

Simplify.

Substitution

Simplify.

Area formulas

area of shaded figure = area of larger rectangle – area of smaller rectangle

Ch 10.5

A. 168 ft2

B. 156 ft2

C. 204 ft2

D. 180 ft2

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.