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Page 1: Geometry 7.1 Area of Triangles and Quadrilaterals.

Geometry

7.1 Area of Triangles and Quadrilaterals

Page 2: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Goals:

Find the area of triangles, parallelograms, rectangles, squares, and trapezoids.

Page 3: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area

The measure of part of a plane surface.

Measured in square units. 10 square inches can be written 10

in2.

Page 4: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Page 5: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Square

s

s

2A s

Page 6: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a rectangle

L

W

A LW

Page 7: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of Parallelogram

h

b

A bh

Page 8: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of Parallelogram

b

h

L

W

Page 9: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Triangle

h

b

12

A bh

Why does this work?

Page 10: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Triangle

h

b

Make a congruent triangle.

Page 11: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Triangle

h

b

Rotate it 180.

Page 12: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Triangle

h

bSlide them together.

Page 13: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Triangle

h

b

This is just a parallelogram.

The triangle is 1/ 2 of this.

Page 14: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Which triangle has the largest area?

A B C

They all have the same area: equal bases and equal heights.

Page 15: Geometry 7.1 Area of Triangles and Quadrilaterals.

April 18, 2023MA 08 Geometry 7.1 Areas of Triangles and

Quadrilaterals

Area of a Trapezoid

b1

b2

h

1 21 ( )2

A h b b


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