Answer:
[tex]19 sq.\ units[/tex]
Step-by-step explanation:
The best way to approach this is to figure out the area of the overall square, then remove any gaps.
The overall square is 5 by 5 so the area is:
[tex]A_t = s * s = 5 * 5 = 25\ sq.\ units[/tex]
There are 5 gaps in the shape of triangles, we will use the formula: [tex]A = \frac{bh}{2}[/tex], and subtract from the total.
1. (Top left)
[tex]A_1 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]
2. (Top right)
[tex]A_2 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]
3. (Bottom left)
[tex]A_3 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]
4. (Bottom center)
[tex]A_4 = \frac{bh}{2} = \frac{2 * 1}{2} = 1[/tex]
5. (Bottom right)
[tex]A_3 = \frac{bh}{2} = \frac{2 * 2}{2} = 2[/tex]
The total triangle area is:
[tex]A = 1 + 1 + 1 + 1 + 2 = 6[/tex]
Subtract from total area to actual area:
[tex]A_s = A_t - A = 25 - 6 = 19 sq.\ units[/tex]
