Holt CA Course 1

10-4 Area of Triangles and Trapezoids

AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).Also covered: AF1.2, AF3.2

California Standards

1 2

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

A. Find the area of the triangle.

Additional Example 1: Finding the Area of a Triangle

5

8

A = 12

bh Use the formula.

A = 12

(8 · 5) Substitute 8 for b and 5 for h.

A = 20

The area of the triangle is 20 square units.

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

B. Find the area of the triangle.

Additional Example 1: Finding the Area of a Triangle

9

A = 12

bh Use the formula.

A = 12

(12 · 9) Substitute 12 for b and 9 for h.

A = 54

The area of the triangle is 54 square units.

12

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

A. Find the area of the triangle.

A = 12

bh Use the formula.

A = 12

(6 · 9) Substitute 6 for b and 9 for h.

A = 27

The area of the triangle is 27 square units.

Check It Out! Example 1

6

9

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

B. Find the area of the triangle.

A = 12

bh Use the formula.

A = 12

(7 · 10) Substitute 7 for b and 10 for h.

A = 35

The area of the triangle is 35 square units.

Check It Out! Example 1

10

7

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

The two parallel sides of a trapezoid are its bases, b1 and b2. The height of a trapezoid is the perpendicular distance between the bases.

h

b1

b2

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

In the term b1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.”

Reading Math

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

A. Find the area of the trapezoid.

Additional Example 2: Finding the Area of a Trapezoid

5 in.

6 in.

9 in.

A = 12

h(b1 + b2) Use the formula.

A = 12

· 6(9 + 5)

A =12

· 6(14)

A = 42

The area of the trapezoid is 42 in2.

Substitute.

Multiply.

Add.

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

B. Find the area of the trapezoid.

Additional Example 2: Finding the Area of a Trapezoid

A = 12

h(b1 + b2) Use the formula.

A = 12

· 7(16 + 12)

A =12

· 7(28)

A = 98

The area of the trapezoid is 98 cm2.

Substitute.

Multiply.

Add.

12 cm

16 cm

7 cm

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

A. Find the area of the trapezoid.

A = 12

h(b1 + b2) Use the formula.

A = 12

· 6(11 + 4)

A =12

· 6(15)

A = 45

The area of the trapezoid is 45 in2.

Substitute.

Multiply.

Add.

Check It Out! Example 2

4 in.6 in.

11 in.

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

B. Find the area of the trapezoid.

A = 12

h(b1 + b2) Use the formula.

A = 12

· 9(5 + 16)

A =12

· 9(21)

A = 94.5

The area of the trapezoid is 94.5 cm2.

Substitute.

Multiply.

Add.

Check It Out! Example 2

16 cm

5 cm

9 cm

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state?

Additional Example 3: Geometry Application

A = 12

h(b1 + b2) Use the formula.

A = 12

· 300(153 + 220)

A =12

· 300(373)

A = 55,950

The area of Wisconsin is approximately 56,000 square miles.

Substitute.

Multiply.

Add.

Holt CA Course 1

10-4 Area of Triangles and Trapezoids

A large preserve has a similar trapezoid shape. What is the approximate area of the preserve?

Check It Out! Example 3

232 mi

116 mi

A = 12

h(b1 + b2)Use the formula.

A = 12

· 129(232 + 116)

A =12

· 129(348)

A = 22,446

The area of the preserve is approximately 22,446 square miles.

Substitute.

Multiply.

Add.

129 mi