Question

A square with an area of 1 square meter is decomposed into 9 identical small squares. Each small square is decomposed into two identical triangles.

a. What is the area, in square meters, of 6 triangles? If you get stuck draw a diagram.

b. How many triangles are needed to compose a region that is 1 1/2 square meters?

(By the way, I need to show my work so I need some answers that have the work in them.)

Answer 1

Dear student,

Answer:a) Area of six triangles = 1/3 m²

b) 27 triangles

Solution:

The area of given square is 1 m².

this square is decomosed into 9 identical square

So each new small square have an area of 1/9 m²

Now each small square further decompsed into two triangles

Area of one triangle = 1/18 m²

Area of identical six triangles = 6 × (1/18) m²

= (1/3) m²

2) if one triangle has 1/18 m² area

n triangle have n× 1/18 m²

To composed an area of 3/2 m² we have to take 27 triangles each having an area of 1/18 m²

Since 27 ×1/18 m²

= 3/2 m²

Hope this helps you.