Tri

Geometry Level 1

Each side of a square is divided into three equal parts by two points on it. The points are then connected by line segments, as shown in the diagram below (that is not drawn to scale).

If the smaller, red square has an area of 800, what is the area of the large square?

The answer is 3600.

3 solutions

Chew-Seong Cheong
Jun 30, 2017

From the figure above, we can see that the four small square in the center make up an area of 800. Therefore, each small square is 200 in area. The triangles (one marked yellow) by the sides is each one half of the small square or two triangles make a small square. Since altogether there are 18 small square the area of the big square $A = 18 \times 200 = \boxed{3600}$ .

I did it the same way but took the red square as my basic unit. Each of the corners need two yellow triangles to match the red square. Thus total area is five time red minus four times yellow, which is 4.5 times red, so 3600.

Anthony Cutler - 3 years, 9 months ago

Linkin Duck
Jun 30, 2017

Let the side of the large square be 3a, then square of the side of the red square is a^2+a^2=800 --> a=20 (Pythagoras' theorem). Hence, the area of the large square=9x20^2=3600.

How did you determine that "square of the side of the red square is a^2 + a^2"?

Calvin Lin Staff - 3 years, 11 months ago

Auro Light
Sep 2, 2017

The side of large square is divided into three equal parts, as shown in diagram. Let each of the small part be ' a ', so the side of large square is 3a.
Let the side of red square be ' b '.
If a triangle is formed at one of the corner of large square, with sides 'a' and 'a', the length of its hypotenuse will be 'b'.
So, we have,
a^2 + a^2 = b^2,
But b^2 = 800,
So, 2a^2 = 800,
a^2 = 400,
Area of large square = (3a)^2 = 9a^2 = 9×400 = 3600.

Tri

The answer is 3600.

3 solutions

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