Deriving the Formula for Area of a Triangle:

Recall the formula for the area of a rectangle: _____________________

To derive the formula for the area of a triangle, follow these steps:

1) Mark a point at the top of the index card.

2) From this point, draw two lines, one to each bottom corner of the index card.

3) Cut along these two lines.

How does the base and height of the triangle relate to the original rectangle?

4) Take the two small pieces of index cards that are remaining and see if you can fit them

on top of the triangle.

What does this tell you about the area of the triangle?

Area of a Triangle

This formula works for any triangle - acute, right, or obtuse. Let’s try a few problems!

1) Find the area of the triangle below. 2) Find the area of an isosceles

triangle with sides 18, 18, and 8

3) Find the area of the triangle below.

15 cm

12 cm

8 mm

7mm

10.1 – Areas of Triangles and Parallelograms 10.1

Discovery

Deriving the Formula for the Area of a Parallelogram:

Recall the formula for the area of a rectangle: _____________________

To derive the formula for the area of a parallelogram, follow these steps:

1) Mark a point at the top of the index card.

2) From this point, draw one line, to the closest bottom corner of the index card.

3) Cut along this line.

4) Translate the cut triangle to the opposite side of the rectangle and tape it to form a

parallelogram.

How does the base and height of the parallelogram relate to the original rectangle?

What does this tell you about the area of the parallelogram

Area of a Parallelogram

Let’s try a few problems!

1) Find the area of a parallelogram 2) 3)

with a base of 16 and height of 8

14

4

60

16

6

135

Arrghhh…..on with the discovery!