Question

Hi! Can you please tell me the answer and explain how to do this (in your own words)? The best answer get's brainiest!

Answer 1

Answer:

$97.5 \ ft^2$

Step-by-step explanation:

1. Find the area of rectangle.

Rectangle:

Width = 12 ft

Length = 5 + 10 = 15 ft

$Area=\text{Length}\times \text{Width}\\ \\=12\cdot 15\\ \\=180\ ft^2$

2. Find the area of two white triangles.

a) Right triangle with legs of 12 ft and 10 ft.

$A_1=\dfrac{1}{2}\times \text{Leg}_1\times \text{Leg}_2\\ \\=\dfrac{1}{2}\cdot 10\cdot 12\\ \\=5\cdot 12\\ \\=60\ ft^2$

b) Right triangle with legs of 5 ft and 12 - 3 = 9 ft.

$A_2=\dfrac{1}{2}\times \text{Leg}_1\times \text{Leg}_2\\ \\=\dfrac{1}{2}\cdot 5\cdot 9\\ \\=\dfrac{1}{2}\cdot 45\\ \\=22.5\ ft^2$

3. Find the area of shaded region:

$A_{shaded}\\ \\=A-A_1-A_2\\ \\=180-60-22.5\\ \\=97.5 \ ft^2$