Question P6 Overlap and cancel
4 identical semicircles overlap in a row. A, B and C are the 3 identical shaded overlaps. The unshaded area is 2125 cm² more than the shaded area. Take π = 3.14. Find (a) the perimeter of the unshaded part, (b) the total shaded area.
See all 8 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See the free ones
65 worked examples are free without a code, two from every pattern. No account, either way.
Sent in by a reader. Send me the one you are stuck on →
Two shapes share a region, and the shared part cancels out.
In this one. An overlap belongs to two shapes at once — so adding all four semicircles counts each shaded part twice, and cutting the shaded parts out turns every arc into an edge.
Shapes are joined, stacked, or have a piece cut off, and the question compares a perimeter or length before and after, rather than asking for an area from scratch.
Children assume perimeter changes the same way area does. Joining shapes or cutting off a corner can leave the perimeter unchanged, or change it by a different amount from the area.
Worked examples of all 33 patterns and skills, in a booklet you can print.