Answer:
Area = 26ft²
Step-by-step explanation:
To solve this problem, we'll have to break the "hole" into its respective shapes so as to make it easy to solve.
In the hole, we have 1 rectangle and two triangles of different dimensions.
1. Rectangle
Area of a rectangle = length * width
Length of the rectangle = 8ft
Width of the rectangle = 3 ft
Area of the rectangle = 8 * 3 = 24ft²
2. Triangle
Area of the triangle = ½(b * h)
b = breadth of the triangle
H = height of the triangle
But since both triangle have the same height, we can calculate of one and use the value for the second one.
Height of the triangle = length of the hole - length of the rectangle
Height of the triangle = 12 - 8 = 4ft
For the first triangle,
The breadth of the triangle is 4 ft
Area of the triangle = ½ ( b * h)
Area = ½ *( 4 * 4)
Area = ½ * 16 = 8ft²
3. Area of the third triangle = ½ (b * h)
Breadth of the second triangle = 3ft
Height of the triangle = 4ft
Area = ½ (4 * 3) = ½ * 12 = 6ft²
Total area of the hole = area of rectangle + area of first triangle + area of second triangle
Total area of the hole = (12 + 8 + 6)ft² = 26ft²
