Comparing Areas

Algebra Level 2

The square given below is divided into 3 rows of equal area. In the top row, the region labelled 'A' has the same area as the region labelled 'B'. In the middle row, the 3 regions have equal areas. In the bottom row, the 4 regions have equal areas. What fraction of the square's area is occupied by the regions marked 'A'?

1 4 \dfrac{1}{4} 1 3 \dfrac{1}{3} 12 13 \dfrac{12}{13} 13 36 \dfrac{13}{36}

Anuj Shikarkhane by Anuj Shikarkhane , 19, India

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2 solutions

Azadali Jivani
Sep 1, 2017

suppose area of sq. = L^2 = 12^2 = 144
so height of each row = 4, length of sq. of top row = 6, length of sq. of middle row = 4 & length of bottom row = 3
Total areas of A(top) + A(middle) +A(bottom) = 6 * 4 + 4 * 4 + 3 * 4 = 52,
Fraction area = 52/144 = 13/36

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Edwin Gray
Sep 8, 2018

Each row has the same area; denote it by x. Total area of regions A = 1/2 of row 1 + 1/3 of row 2 + 1/4 of row 3. The fraction which is A is (x/2 + x/3 + x/4)/3x = 13x/36x = 13/36. Ed Gray

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