A geometry problem by Titas Biswas

Geometry Level 1

in the given figure, all line segments of the shaded portion are of same length and at right angles to each other. What is the area of the shaded portion?

Problem Source : http://www.mrunal.org

48 46 52 42

2 solutions

Peter Michael
Jul 22, 2015

To attain the area of the entire shape multiply the sides together: $10cm*10cm = 100cm^2$ .
Because all the edges of the coloured portions are of the same length take: $10cm/5=2cm$ .
Now since each red square is $4cm^2$ and there are 13 of them in total we can evaluate: $100cm^2-13*4cm^2 = 52cm^2$ .

Thanks for posting the problem Titas!

Moderator note:

Note the errors in the last paragraph. Are you counting the red squares or the white square? It should be $100 - 12 \times 4 = 52$ .

I think the easier approach would be to count the number of red squares directly.

You are welcome. :) Glad that you liked solving it and the solution is perfect.

Titas Biswas - 5 years, 10 months ago

A Former Brilliant Member
Oct 28, 2017

The side length of one square is $\dfrac{10}{5}=2$ . There are $13$ squares with side length of $2$ . So the area of the red portion is $13(2^2)=$ $\boxed{52}$

A geometry problem by Titas Biswas

2 solutions

Moderator note:

0 pending reports