Question

A square with 1 square meter is decompose into 9 identical small squares. Each small square is decomposed into identical triangles. What is the area , in square meters, of 6 triangles ? How many triangles are needed to compose a region that is 1.5 square meters?

Answer 1

A square is given with an area of 1 square meter.

Area of square = $s \times s$

1 = $s^2$

s = 1 m

Now, this square is decomposed into 9 identical small squares.

Square with area of 1 square meter = 9 $\times$ area of small squares

1 = 9 $\times x^2$

$x^2 = \frac{1}{9}$

x = $\frac{1}{3}$

So, side of smaller square is $\frac{1}{3}$ meter.

Now, square is decomposed into two triangles.

Area of one triangle = $\frac{1}{2} \times base \times height$

= $\frac{1}{2} \times \frac{1}{3} \times \frac{1}{3}$

= $\frac{1}{18}$ square meter

Now, Area of 6 triangles = $6 \times \frac{1}{18}$

= $\frac{1}{3}$ square meter.

Number of triangles needed to compose a region that is 1.5 square meters

= $1.5 \div \frac{1}{18}$

= 1.5 $\times 18$

= 27 triangles.

Therefore, 27 triangles are needed to compose a region that is 1.5 square meters.

Answer 2

Answer:

meter.

Area of square = s \times ss×s

1 = s^2s

2

s = 1 m

Now, this square is decomposed into 9 identical small squares.

Square with area of 1 square meter = 9 \times× area of small squares

1 = 9 \times x^2×x

2

x^2 = \frac{1}{9}x

2

=

9

1

x = \frac{1}{3}

3

1

So, side of smaller square is \frac{1}{3}

3

1

meter.

Now, square is decomposed into two triangles.

Area of one triangle = \frac{1}{2} \times base \times height

2

1

×base×height

= \frac{1}{2} \times \frac{1}{3} \times \frac{1}{3}

2

1

×

3

1

×

3

1

= \frac{1}{18}

18

1

square meter

Now, Area of 6 triangles = 6 \times \frac{1}{18}6×

18

1

= \frac{1}{3}

3

1

square meter.

Number of triangles needed to compose a region that is 1.5 square meters

= 1.5 \div \frac{1}{18}1.5÷

18

1

= 1.5 \times 18×18

= 27 triangles.

Therefore, 27 triangles are needed to compose a region that is 1.5 square meters.