Area of 2D shapes

Quadrilaterals

• A quadrilateral is a geometric figure that is made up of four line segments, called sides, that intersect only at their endpoints.

What are parallel lines?

Two lines that never intersect.

Special Quadrilaterals

• Trapezoid– A quadrilateral with exactly

1 pair of parallel sides.

• Parallelogram– A quadrilateral with 2 pairs

of parallel sides.

What is the area of this parallelogram?

PARALLELOGRAM

CUT HERE!

S=side H=height

B=base

What is the area of this parallelogram?

PARALLELOGRAM

MOVE TO HERE!

B=base

H=height

It’s the same as the area of this rectangle!

PARALLELOGRAM

H=height

B=base

Areaparallelogram = Base x Height(perpendicular height H)

PARALLELOGRAM

B=base

Side

H=height

To find the area of a parallelogram, you always multiply the base and the height.

So, Area = base x height or A = bh

Remember: The height is the line segment that is perpendicular to the

base and creates a right angle.12 in

10 in

10 in

What is the area of this parallelogr

am?Area = base x height

A = (10)(10)A = 100 in²

Your TurnFind the area and perimeter of the

parallelogram.

24 cm

12 cm

A=bhA= 12(24)A=288 cm²

14 cm

P = 12+12+14+14

P = 52 cm

Area of a Triangle

1

2

Area of parallelogram = base x heightArea of triangle = base x height

2

1

Area = bh

2

1

Finding the Area of a Triangle

1. Write the formula for area of a triangle.

2. Substitute in values.

3. Simplify.

11 ft

23 ft

2

1

A= bh

2

1

A= (23)(11)

A= 126.5 ft²

You try!Find the area and perimeter of the

triangle.

17 m

13.4 m A= bh

A= (17)(13.4)

A= 113.9 m²

2

1

2

1

20 m 15 m

P = 20+15+17P = 52 m

Given the formula for the area of a parallelogram we are going to use that information to discover the

formula for the area of a trapezoid.

Watch carefully not to miss it!

Notice that the trapezoid is half the area of the parallelogram.

(b1 + b2)

h

Copy the trapezoid, flip it over, and put it next to the original. It makes a parallelogram.

We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.

(b1 + b2)

h

Parallelogram

Trapezoid

Notice that the trapezoid is half the area of the parallelogram. How do we find

half the area?

A = (b1 + b2) • h

Hint: Think of area of a triangle.

hbA 2

1

Area of Trapezoid

2 in

6 in

3 in A = (b1 + b2) • h

4 in

2

1

A = (2 + 6) • 32

1

A = (8) • 32

1

A = 4 • 3A = 12 in²

4 in

Perimeter of Trapezoid

P = 4 + 4 + 2 + 6P = 16 in

Area of Trapezoid

3 m

8 m

4 m 5 m A = (b1 + b2) • h

2

1

A = (3 + 8) • 42

1

A = (11) • 42

1

A = (44)

A = 22 m²

2

1

Practice!