Answer:
[tex]97.5 \ ft^2[/tex]
Step-by-step explanation:
1. Find the area of rectangle.
Rectangle:
Width = 12 ft
Length = 5 + 10 = 15 ft
[tex]Area=\text{Length}\times \text{Width}\\ \\=12\cdot 15\\ \\=180\ ft^2[/tex]
2. Find the area of two white triangles.
a) Right triangle with legs of 12 ft and 10 ft.
[tex]A_1=\dfrac{1}{2}\times \text{Leg}_1\times \text{Leg}_2\\ \\=\dfrac{1}{2}\cdot 10\cdot 12\\ \\=5\cdot 12\\ \\=60\ ft^2[/tex]
b) Right triangle with legs of 5 ft and 12 - 3 = 9 ft.
[tex]A_2=\dfrac{1}{2}\times \text{Leg}_1\times \text{Leg}_2\\ \\=\dfrac{1}{2}\cdot 5\cdot 9\\ \\=\dfrac{1}{2}\cdot 45\\ \\=22.5\ ft^2[/tex]
3. Find the area of shaded region:
[tex]A_{shaded}\\ \\=A-A_1-A_2\\ \\=180-60-22.5\\ \\=97.5 \ ft^2[/tex]
