# Math Help - [SOLVED] Find the areas of the square

1. ## [SOLVED] Find the areas of the square

Note: Figure not drawn to scale

In the figure, what is the area of the square with the darken borders?

page 721 #16

2. Hello, fabxx!

In the figure, what is the area of the inner square?
Code:
            2        1
*-----------*-----*
1 |       *    *    |
|   *         *   |
*              *  | 2
|*              * |
| *              *|
2 |  *              *
|   *         *   |
|    *    *       | 1
*-----*-----------*
1        2

It is a square within a square.
. . The four right triangles are congruent.

In a right triangle, the legs are 1 and 2.
. . Hence, the hypotenuse is $\sqrt{5}$

Therefore, the area of the inner square is: . $\left(\sqrt{5}\right)^2 \;=\;5$ square units.

3. Area of outside square=9

Now find the area of the triangles
they all have an area of 1
so all triangles put together have an area of 4

9-4=5

the area of the inside square is 5

instead of using pythagoras, you could just understand that the area of a right triangle is (length x height)/2

4. Hello, Mike!

An excellent solution!

5. Thanks mikedwd and Soroban. You guys are great!