6th Grade Math Textbook, Fundamentals

&KDSWHU 

Method 2: Adopt a Different Point of View

You can move the smaller triangle around within the

larger triangle without changing the area of the region

between the triangles.

As shown in the figure below, if you move the smaller

triangle down so that its lower left vertex corresponds

with the lower left vertex of the outside triangle, the

shaded region becomes a trapezoid with b 1 16 m,

b 2 8 m, and h6 m.

To find the area of the trapezoid, use the area formula

for a trapezoid.

A h(b 1 b 2 )

 (16 cm 8 cm) (3 cm)(24 cm)

72 cm^2

Check to make sure your answer makes sense.

You can move the inside triangle as shown in the figure below

to create a different trapezoid.

The area of the trapezoid is

A (8 m)(6 m 12 m) 72 m^2.

This is the same answer as the one above.

So the answer checks.

1

(^21)
3
(cm) 6
1
2
1
2
12 m
8 m
8 m
6 m
16 m
6 m
12 m
8 m
16 m
12 m
8 m
6 m 6 m
16 m
6 m
12 m
8 m
3UDFWLFH $FWLYLWLHV
Lesson 12-9 for exercise sets.