9-2 Area of Triangles and Trapezoids

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9-2 Area of Triangles and Trapezoids

Warm Up

1. True or false: If the height of a rectangle equals the base of a parallelogram and the base of the rectangle equals the height of the parallelogram, then the rectangle and the parallelogram have the same area.

2. Find the area of a rectangle with a length of 53 in. and a width of 47 in.

True

2,491 in2

9-2 Area of Triangles and Trapezoids

Problem of the Day

3/$5.00

Which is a better deal, 3 discs for $5.00 or 4 discs for $7.00?

9-2 Area of Triangles and Trapezoids

MA.6.A.3.4 Solve problems given a formula.

Also MA.6.A.4.2, MA.6.G.4.3

Sunshine State Standards

9-2 Area of Triangles and Trapezoids

You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.

9-2 Area of Triangles and Trapezoids

9-2 Area of Triangles and Trapezoids

Find the area of the triangle.

Additional Example 1: Finding the Area of a Triangle

A = 12

bh Write the formula.

A = 12

(20 · 12) Substitute 20 for b and 12 for h.

A = 120

The area is 120 ft2.

A = 12

(240) Multiply.

9-2 Area of Triangles and Trapezoids

An altitude of a triangle is a perpendicular segment from one vertex to the line containing the opposite side. The length of the altitude is the height.

Reading Math

9-2 Area of Triangles and Trapezoids

Check It Out: Example 1A

Find the area of the triangle.

11 cm

4 cm

A = bh

= (11 • 4) = 22 cm

212

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__

2

2

9-2 Area of Triangles and Trapezoids

The diagram shows the floor plan for a triangulardining area. What is the area of the floor?

Check It Out: Example 1B

6.2 m

A = 12

bh

= 12

( 34.8 • 6.2) = 107.88 2m

34.8 m

9-2 Area of Triangles and Trapezoids

The diagram shows the section of a forest being studied. What is the area of the section?

Additional Example 2: Application

A = 12

bh Write the formula.

A = 12

(43.9 • 16) Substitute 43.9 for b. Substitute 16 for h.

A = 351.2

The area is 351.2 km2.

A = 12

(702.4) Multiply.

9-2 Area of Triangles and Trapezoids

Check It Out: Example 2AMitch uses the piece of wood shown as part of a skateboard ramp. Its area is 0.8 m .

What is the height of the piece of wood?.

A = bh;

0.8 = (2)

0.8 = h

The height is 0.8 m.

h12

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__

2

2 m

2

9-2 Area of Triangles and Trapezoids

Check It Out: Example 2B

Mitch wants his skateboard ramp to be at least 750 cm tall. Should he use this piece of wood to build the ramp? Explain.?.

Yes; the height is 0.8 m or 800 cm, which is greater than 750 cm.

9-2 Area of Triangles and Trapezoids

9-2 Area of Triangles and Trapezoids

Find the area of the trapezoid.

Additional Example 3: Finding the Area of a Trapezoid

A = 12

h(b1 + b2) Use the formula.

A = 53

The area is 53 yd2.

Multiply.

A =12

· 4(26 )12

Substitute 4 for h, 14 for b1, and 12 for b2.

12

A = 12

· 4(14 + 12 )12

9-2 Area of Triangles and Trapezoids

Check It Out: Example 3A

Lisa wants to cut a hole in the shape of a trapezoid out of a piece of wood. The figure shows her plans, and each square of the grid represents 1 ft . What is the area of the remaining wood after she cuts out the hole?

2

9-2 Area of Triangles and Trapezoids

Check It Out: Example 3A continued

5 × 8 = 40;

The remaining area is 26.5 ft .240 - 13.5 = 26.5

(3 + 6)3 = 13.5;12_

9-2 Area of Triangles and Trapezoids

Check It Out: Example 3B

The figure shows a vegetable garden that is planted with squash and carrots. To the nearest percent, how much of the vegetable garden is for squash?

9-2 Area of Triangles and Trapezoids

Check It Out: Example 3B continued

About 43% of the vegetable garden is for squash.

(8 + 6)3 = 21; (6)(3) = 9; = , or about 0.43921_ 3

7_1_

21_2