Question P5 Overlap and cancel
Today’s problem — free all day, every step. Every day has one.
A rectangular library hall JKLM is divided into two reading rooms by a glass partition NO, where N is on JK and O is on ML (so JNOM and NKLO are the two rooms). E is a bookshelf on JM, F is a bookshelf on KL, and W is the midpoint of NO. The perimeter of JKLM is 88 m and JM : JK = 5 : 6. Find (a) JM, and (b) the total area of the shaded triangles EWO and NWF.
Answer
See all 7 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.
Two shapes share a region, and the shared part cancels out.
In this one. The triangles have equal bases on the two halves of NO, while their perpendicular heights add to the full width JK, so the partition's position does not affect their total area.
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.