An Area Problem(easier)

Geometry Level 2

The black square the shapes are inscribed in has the area of $25cm^2$ . $H$ is the midpoint of $AG$ . $F$ is the midpoint of $GE$ . $D$ is the midpoint of $CE$ . $B$ is the midpoint of $AC$ . 4 parts of the circumference of the circle touch the square. Which shape has the larger area?

Impossible to tell The circle The pentagon They are the same

2 solutions

Gerard Boileau
Jan 8, 2019

The area of the black square is 25, so the side is 5. The area of the circle is (5/2)^2 * π which is about 19.635.

The red area is made of 5 times triangle AHB. The area of this triangle is (5/2)^2 * 1/2, i.e. 25/8. The red area is 5 * 25/8, i.e. 15.625.

The area of the circle is the greatest.

Justin Arun
May 30, 2018

The side of the square is 8cm. So the area of the circle is $16π$ , which is about $50.265cm^2$ . The square's area is $32+8=40cm^2$

That isn't a square,I think.It has 5 sides.

X X - 3 years ago

Thanks-I changed that. I know-I've made that mistake TWICE

Justin Arun - 3 years ago

An Area Problem(easier)

2 solutions

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