Area Of A Trapezoid

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# Area Of A Trapezoid - PowerPoint PPT Presentation

b2. h. b1. Area Of A Trapezoid. There are six different ways to calculate the area of a trapezoid. Half parallelogram Rectangle/triangle Parallelogram & Triangle Parallelogram Rectangle Two Triangles. b2. b2. h. 1/2h. b1. b1. Area Of A Trapezoid. Start with a trapezoid.

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## PowerPoint Slideshow about 'Area Of A Trapezoid' - tahirah

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Presentation Transcript

b2

h

b1

Area Of A Trapezoid

There are six different ways to calculate the area of a trapezoid

• Half parallelogram
• Rectangle/triangle
• Parallelogram & Triangle
• Parallelogram
• Rectangle
• Two Triangles

b2

b2

h

1/2h

b1

b1

Area Of A Trapezoid

Draw the segment connecting the midpoints of the legs.

Area Of A Trapezoid

Rotate the top section of the trapezoid and then move it to line up with the bottom half.

1/2h

b1

b2

Home

Area Of A Trapezoid

The area now is the area of a parallelogram

In this case the base of the parallelogram is b1+b2 and the height is only half of the original height.

b2

h

b2

b1

h

b1

Area Of A Trapezoid

Split the trapezoid into a rectangle and two triangles

Home

Area Of A Trapezoid

b2

h

h

b1-b2

b2

So the area of the trapezoid is now the area of the two triangles put together plus the area of the rectangle

Giving the formula…?

b2

b2

h

h

b1

b1

Area Of A Trapezoid

Split the trapezoid into a parallelogram and a triangle

Home

Area Of A Trapezoid

b2

h

h

b2

b1-b2

The area of the trapezoid is now the area of the parallelogram plus the area of the triangle.

Giving the formula…?

b2

h

b1

Area Of A Trapezoid

Take the trapezoid and copy it.

b2

h

b1

Area Of A Trapezoid

Rotate the image and then move it to line up with the other trapezoid

b2

h

b1

Home

Area Of A Trapezoid

b1

b2

So the area of this trapezoid is ½ of the parallelogram.

parallelogram:

Giving the formula…?

b2

1/2h

b1

Area Of A Trapezoid

Find the midpoint of each leg.

From each midpoint, drop a perpendicular to the longer base, forming right triangles.

b2

b1

Area Of A Trapezoid

Rotate the right triangles to form a rectangle.

h

b

Home

Area Of A Trapezoid

Rectangle:

So the area is now the area of the rectangle. Find the width.

Giving the formula…?

b2

b2

h

h

b1

b1

Area Of A Trapezoid

Draw in a diagonal forming two triangles.

Home

Area Of A Trapezoid

b2

h

h

Triangle 2:

Triangle 1:

b1

The Area is the sum of the two triangles

Giving the formula…?

Area Of A Trapezoid

The area of a trapezoid can be calculated many ways, but in the end they all come up with the same formula can you guess what formula it is?