Did you know?
The area of an irregular figure can be found by breaking it down into more familiar shapes and calculating the area of each shape individually.
In this case, the irregular figure consists of a triangle and a semi-circle. By finding the area of each shape and summing them up, we can determine the total area of the figure.
To find the area of the triangle, we use the formula:
Area = (base x height) / 2
In the given image, the base of the triangle is the length between the semi-circle diameter side and the opposing triangle, which is 4.8 feet. The height can be found by drawing a line from the vertex opposite the semi-circle side to the base. This line bisects the vertex, creating two right triangles. The height of one of these right triangles can be found using the Pythagorean theorem, as follows:
a^2 + b^2 = c^2
Where a = 3.6 feet (the radius of the semi-circle) and b = (4.8 feet / 2) = 2.4 feet (half the length of the base of the triangle).
Substituting the values into the equation, we have:
(3.6 feet)^2 + (2.4 feet)^2 = c^2
12.96 feet^2 + 5.76 feet^2 = c^2
18.72 feet^2 = c^2
c ≈ 4.33 feet
Since the height is the perpendicular distance from the base to the opposing vertex, we can use this value (4.33 feet) as the height.
Now, to find the area of the triangle:
Area = (4.8 feet x 4.33 feet) / 2
Area ≈ 10.38 square feet
Moving on to the semi-circle, we can find its area using the formula:
Area = πr^2
Given that the diameter of the semi-circle is 3.6 feet, the radius (r) is half of that, which is 1.8 feet.
Area = 3.14 x (1.8 feet)^2
Area ≈ 10.17 square feet
Finally, to find the total area of the irregular figure, we add the areas of the triangle and the semi-circle:
Total area ≈ 10.38 square feet + 10.17 square feet
Total area ≈ 20.55 square feet
Rounding to the nearest tenth, the area of the irregular figure is approximately 20.6 square feet.
