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.

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.

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

Quadrilaterals

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

Quadrilaterals

Area of a Square

s

s

2A s

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

Quadrilaterals

Area of a rectangle

L

W

A LW

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

Quadrilaterals

Area of Parallelogram

h

b

A bh

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

Quadrilaterals

Area of Parallelogram

b

h

L

W

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?

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

Quadrilaterals

Area of a Triangle

h

b

Make a congruent triangle.

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

Quadrilaterals

Area of a Triangle

h

b

Rotate it 180.

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

Quadrilaterals

Area of a Triangle

h

bSlide them together.

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.

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.

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