Area: Parallelograms, Triangles, and

Trapezoids

Written ByMrs. Ballard

Tweaked By KLS

• Perimeter – the distance around a figure

• To find perimeter: add all the sides

• Area – the amount of surface a figure covers

• To find area use the correct area formula

• Perimeter & circumference units are always to the first power.

• Area & surface area units are always squared.

• Volume units are always cubed.

Units

Area of Rectangle: A = LW

Ex. 1 Find the area of a rectangle with length 8 cm and width 4 cm.

• Area of Square: A = s2 (s equals a side)

Ex. 2 Find the area of the square below.

10 in

x

y

Area of Parallelograms: A = bh

• Height is the perpendicular line that connects the parallel sides.

h

b

b

Ex. 3 Find the area:

2.6 cm

7.3 cm

x

y

Ex. 4 If the area of the parallelogram is 136 cm2 and the base is 13.6 cm, find the height.

Megan wants a plastic cover for the pool to keep her dog from playing in it. The best price for the cover she can find is $3.25 per square foot. How much will the plastic cover cost if the pool is 20 feet by 14 feet

Nicole wants to build a square game court. She needs a ground area of at least 49 sq ft. In the back yard, there is a space 10 ft wide by 16 ft long. Does Nicole have enough room to build the game court? If yes, what is the largest area the game court can have?

Jorge and Merrick are trying to figure out who has the larger bedroom. Jorge’s room is long and narrow. Merrick’s room is square. If Jorge’s room is 8 ft by 14 ft and Merrick’s room is 16 ft wide, whose bedroom is larger? How much larger?

The outside dimensions of a picture frame are 3 ft by 29 inches. If its inside dimensions are 1 2/3 ft by 25 inches, what is the area of the frame?

Area of Triangles : A = ½ bh A = 0.5bh

Base can be any side of the triangle; usually the side that the triangle is sitting on.

Height must be at a right angle to the base.

Height is also known as the altitude.

base

base

base

height

height

height

Ex. 6 Find the area of the triangle below.

9 m2.9 m

8.1 m

Ex. 5 Find the area of a right triangle 9 cm tall and 5 cm long.

Ex. 7 A farmer divided his plot into two equal triangular sections. Find the area of each of the new sections.

39 m

37 m

Area of Trapezoid : A = ½h(b1 + b2) A = 0.5h(b1 + b2)

h is the line perpendicular to both bases

b1 and b2 are the parallel sides of the trapezoid.

legleg

base

base

height

Ex. 8 Find the area of the trapezoid

28 in

38 in

6 in 9 in

Find the area.

28

13 6

16 14

You find the area of the two separate trapezoids.