Regular/irregular regions

1. Find the area of the rectangle.

   2 marks

2. Find the area of this joined-square region.

   2 marks

3. Two non-overlapping rectangles have areas 14 ${\mathrm{cm}}^2$ and 9 ${\mathrm{cm}}^2$. Find the combined area.

   2 marks
4. A rectangle is 7 cm long and 5 cm wide. Find its area.

   2 marks
5. A 5 cm by 4 cm rectangle has a 2 cm by 1 cm corner removed. Find the area left.

   3 marks
6. A student splits a 6 cm by 3 cm rectangle into two pieces and says their areas total 21 ${\mathrm{cm}}^2$. Explain why this cannot be right.

   3 marks

Equivalent correct methods earn the corresponding marks. Include units where asked.

1. Find the area of the rectangle.

   2 marks

   There are 4 squares in each of 3 rows.

   $4\times 3=12$ ${\mathrm{cm}}^2$.

   12 ${\mathrm{cm}}^2$
2. Find the area of this joined-square region.

   2 marks

   Rows contain 5, 3 and 3 squares.

   $5+3+3=11$ ${\mathrm{cm}}^2$.

   11 ${\mathrm{cm}}^2$
3. Two non-overlapping rectangles have areas 14 ${\mathrm{cm}}^2$ and 9 ${\mathrm{cm}}^2$. Find the combined area.

   2 marks

   $14+9=23$ ${\mathrm{cm}}^2$.

   23 ${\mathrm{cm}}^2$
4. A rectangle is 7 cm long and 5 cm wide. Find its area.

   2 marks

   $7\times 5=35$ ${\mathrm{cm}}^2$.

   35 ${\mathrm{cm}}^2$
5. A 5 cm by 4 cm rectangle has a 2 cm by 1 cm corner removed. Find the area left.

   3 marks

   Full area: $5\times 4=20$ ${\mathrm{cm}}^2$.

   Removed area: $2\times 1=2$ ${\mathrm{cm}}^2$.

   $20-2=18$ ${\mathrm{cm}}^2$.

   18 ${\mathrm{cm}}^2$
6. A student splits a 6 cm by 3 cm rectangle into two pieces and says their areas total 21 ${\mathrm{cm}}^2$. Explain why this cannot be right.

   3 marks

   $6\times 3=18$ ${\mathrm{cm}}^2$.

   Splitting does not change the covered surface.

   The original area is 18 ${\mathrm{cm}}^2$, so a correct split must also total 18 ${\mathrm{cm}}^2$. The student may have overlapped or miscalculated pieces.