Question

Find the area of the square below. Each unit on the grid represents one unit. Make sure you show your work and/or explain how you solved it.

Answer 1

Area of the rectangle A = 17 units²

Explanation:

Area of the rectangle A = Area of rectangle ACEG - (Area of the triangle ABH + Area of triangle BCD + Area of triangle DEF + Area of the triangle FGH )

Area of rectangle ACEG = Length × Width

= (5 units) × (5 units)

= 25 square units

Area of the triangle ABH =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(4)(1)`

= 2 units²

Area of the triangle BCD =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(1)(4)`

= 2 units²

Similarly, area of the triangle DEF = 2 units²

And area of the triangle FGH = 2 units²

Now area of the rectangle A = 25 - (2 + 2 + 2 + 2)

= 25 - 8

= 17 square units

Therefore, area of the rectangle A = 17 square units