Problem 4 · 2014 Math Kangaroo
Easy
Geometry & Measurement
area-fraction
The area of rectangle ABCD in the diagram is 10. M and N are the midpoints of the sides AD and BC respectively. What is the area of the quadrilateral MBND?
Show answer
Answer: B — 5
Show hints
Hint 1 of 2
M and N are midpoints, so segment MN splits the rectangle into two equal halves.
Still stuck? Show hint 2 →
Hint 2 of 2
Compare the quadrilateral MBND with the half of the rectangle that contains it.
Show solution
Approach: use the midpoint line to halve the area
- Because M and N are the midpoints of the two opposite sides, the segment MN cuts the rectangle into two equal pieces, each of area 5.
- The quadrilateral MBND is built symmetrically about MN, and a quick shear/area argument shows it covers exactly half of the whole rectangle.
- Half of 10 is 5.
Mark:
· log in to save