6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-7

h

b

Key Concept

Area of a Triangle

A bh, where bis the

base and his the height

1

2

base

height

base

height

Key Concept

Area of a Trapezoid

A (b 1 b 2 )h, where b 1 and b 2 are the

bases and his the height

The bases of a trapezoid are not always

horizontal lines, but they are always

parallel lines.

1

2

13 cm

6 cm

h

b 1  b 2

b 2 b 2  b 1

b 1

h

Area of Triangles and Trapezoids

Objective To use a formula to find the area of a triangle• To use a formula to find the

area of atrapezoid • To rename area units in equivalent forms• To find an unknown base

or height given the area of a triangle or a trapezoid

The area formula for a parallelogram can help you understand
the area formulas for a triangle and for a trapezoid.

You can put any two congruent triangles together to form a

parallelogram, as shown in the figure. The base and the height

of each triangle are the same as the base and the height of the

parallelogram. You can see that the area of each triangle is half

the area of the parallelogram. Since the area of a parallelogram

is Abh, the area of a triangle is A.

The base of a triangle can be any one of its sides.

The altitude is the perpendicular line segment from

a vertex to the base opposite that vertex. The height

is the length of the altitude. As with parallelograms,

the height may be determined by dropping a

perpendicular line segment from a vertex to an

extension of the base that is opposite that vertex.

• Find the area of the triangle at the right.

A bh A (13)(6)

 (78) 39 cm^2

You can put two congruent trapezoids together

to form a parallelogram. The height of the

parallelogram is the same as the height of either

trapezoid. The base of the parallelogram equals

the sum of the bases of either trapezoid. The bases

of a trapezoid are the parallel sides. The height is

the length of a perpendicular line segment from

one base to the other. The area of each trapezoid

equals half the area of the parallelogram. Since

the area of that parallelogram is (b 1 b 2 )h, the

area of the trapezoid is.

• Find the area
  of the trapezoid.

A (b 1 b 2 )h A (7. 413.6)7

 (21)7

 (147) 73.5 mm^2

1

2

1

2

1

2

1

2

(b 1 b 2 )h

2

1

2

1

2

1

2

bh

2

b 2  13.6 mm

b 1  7.4 mm

h  7 mm