Museums The Rock and Roll Hall of Fame and Museum in Cleveland, Ohio, has a triangular shaped wall. What is the area of the wall?

In the Real World

Areas of Triangles and Trapezoids11 5.

Museums The Rock and Roll Hall of Fame and Museum in Cleveland, Ohio, has a triangular shaped wall. What is the area of the wall?

In the Real World

Areas of Triangles and Trapezoids11 5.

You can use the base and height of a triangle to find the area of the triangle. The base of a triangle is the length of any one of the sides. The height of a triangle is the perpendicular distance between the side whose length is the base and the vertex opposite that side.

height

base

NOTE BOOK

Words The area A of a triangle is half the product of a base and the corresponding height.

Algebra

Area of a Triangle

Areas of Triangles and Trapezoids11 5.

A =12

bh

height h

base b

12

= bh

Areas of Triangles and Trapezoids

Finding the Area of a TriangleEXAMPLE 1

To find the area of the wall of the Rock and Roll Hall of Fame and Museum previously described, use the diagram shown.

11 5.

A =12

bh

(231)

= 12,820.5

ANSWER The area of the wall is 12,820.5 square feet.

(111)

Write formula for area of a triangle.

Substitute 231 for b and 111 for h.

Multiply.

111 ft

231 ft

12

A = b h

Areas of Triangles and Trapezoids

Finding the Base of a TriangleEXAMPLE 2

A triangle has a height of 10 centimeters and an area of 35 square centimeters. Find the base of the triangle.

11 5.

ANSWER The base of the triangle is 7 centimeters.

12

A = b h

35 = 5b

7 = b

Substitute 35 for A and 10 for h.

Simplify.

Divide each side by 5.

Write formula for area of a triangle.

35 (10)

Areas of Triangles and Trapezoids11 5.

Trapezoids You can use the bases and the height of a trapezoid to find the area of the trapezoid. The lengths of the parallel sides of a trapezoid are the bases of the trapezoid. The height of the trapezoid is the perpendicular distance between the bases.

height

base 1

base 2

Areas of Triangles and Trapezoids

NOTE BOOK

Words The area A of a trapezoid is half the product of the sum of the bases and the height.

Algebra

Area of a Trapezoid

11 5.

base b 1

base b 2

height h

12

(b 1 + b 2)hA =

12

(b 1 + b 2)hA =

Areas of Triangles and Trapezoids

Finding the Area of a TrapezoidEXAMPLE 3

Find the area of the trapezoid shown.

11 5.

12

(b 1 + b 2)hA =

5 ft

10 ft

8 ftWrite formula for area of a trapezoid.

= 60

ANSWER The area of the trapezoid is 60 square feet.

Substitute 5 for b 1, 10 for b 2 , and 8 for h.

Simplify.

(5 + 10) 8

12

(b 1 + b 2)hA =

Areas of Triangles and Trapezoids

Finding the Height of a TrapezoidEXAMPLE 4

A trapezoid has an area of 66 square meters. The bases are 8 meters and 14 meters. Find the height.

11 5.

12

(b 1 + b 2)hA =

(8 + 14)h66

12

(22)h66 =

66 = 11h

6 = h

ANSWER The height of the trapezoid is 6 meters.

Write formula for area of a trapezoid.

Substitute 66 for A, 8 for b 1, and 14 for b 2.

Add.

Multiply.

Divide each side by 11.