You may also like

problem icon


Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

problem icon

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

problem icon

Kissing Triangles

Determine the total shaded area of the 'kissing triangles'.

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.