Answer:
1140 ft²
Step-by-step explanation:
The area of the gray shaded region using the formula:
[tex]\sf \textsf{Area of shaded region} = \textsf{Area of rectangle} - \textsf{Area of triangle} [/tex]
Given that the dimensions of the rectangle are [tex]\sf 50[/tex] feets in length and [tex]\sf 30[/tex] feets in width:
[tex]\sf \textsf{Area of rectangle} = \textsf{length} \times \textsf{width} = 50 \times 30 [/tex]
Next, the triangle is within the rectangle.
The formula for the area of a triangle is:
[tex]\sf \dfrac{1}{2} \times \textsf{base} \times \textsf{height} [/tex]
In this case, the base is [tex]\sf 24[/tex] feets, and the height is [tex]\sf 30[/tex] feets:
[tex]\sf \textsf{Area of triangle} = \dfrac{1}{2} \times \textsf{base} \times \textsf{height} = \dfrac{1}{2} \times 24 \times 30 [/tex]
Now, substitute these values into the formula for the area of the shaded region:
[tex]\sf \textsf{Area of shaded region} = \textsf{Area of rectangle} - \textsf{Area of triangle} [/tex]
[tex]\sf = 50 \times 30 - \dfrac{1}{2} \times 24 \times 30 [/tex]
Let's perform the calculations:
[tex]\sf \textsf{Area of shaded region} = 1500 - 360 [/tex]
[tex]\sf \textsf{Area of shaded region} = 1140 [/tex]
So, the area of the gray shaded region is 1140 square feet.
