If each diagonal of a square has length 2 , then the area of the square is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
If each diagonal of a square has length 2 , then the area of the square is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

## Solution

We draw the square and its two diagonals.

The diagonals of a square cut each other into two equal parts, and intersect at right angles. So we can decompose the square into 4 identical triangles with base 1 and height 1 . So the area of the square is $4\left[\frac{1}{2}(1)(1)\right]=4\left[\frac{1}{2}\right]=2$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-396.jpg?height=306&width=309&top_left_y=1365&top_left_x=1388)

ANSwER: (B)