Question

I'm a 7th grader so please teach me as such not like a college professor..

Answer 1

Given:

Using the board given, each square is assumed to have an area of 1 square unit.

Hence, to make a square with an area of 9 square units, 9 boxes are selected as shown.

a)

The length of the square is 3 units.

The width of the square is 3 units.

b) Notice the length and the width of the square are the same.

Hence, the length of side (s) of the square is the same.

Therefore, the formula for the area of square is;

`\begin{gathered} A=l* w \\ But\text{ }l=w=s \\ \\ A=s* s \\ A=s^2 \end{gathered}`

c) Drawing a diagonal in the square;

d) Drawing a diagonal in the square makes two congruent shapes which is a triangle. Two congruent right triangles are formed.

e) The area of one triangle is 4.5 square units.

Explanation from the board:

`\begin{gathered} A=1+1+1+(1)/(2)+(1)/(2)+(1)/(2) \\ A=3+1(1)/(2) \\ A=4(1)/(2)\text{ square units} \\ A=4.5\text{ square units} \end{gathered}`