You may also like

Hallway Borders

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Boxed In

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

Nested Squares

Age 11 to 14 Short
Challenge Level

Splitting the diagram into one-inch squares
The largest square is 4 squares long, and the smallest square in the middle is 2 squares long.

Then, we can put the shaded pieces together to make whole square inches.

So there are 5 shaded squares, out of 16 squares in total.

So the proportion of the area which is shaded is $\frac5{16}$.

Finding the areas of the squares
The whole diagram is a 4 inch by 4 inch square, so has area 4$\times$4 = 16 square inches.

The shaded part is contained within a 3 by 3 square, so has area 3$\times$3 = 9 square inches.

 There is a hole in the shaded part, which is a 2 by 2 square. So the area of the hole is 2$\times$2 = 4 square inches.

So the area of the shaded part is
9$-$4 = 5 square inches.

So the proportion of the area which is shaded is $\frac5{16}$.

You can find more short problems, arranged by curriculum topic, in our short problems collection.