Jackson is creating a water garden surrounded by a triangular patch of grass. If the pond will take up the space indicated by the circle, how many square feet of sod will he need to complete the garden (use 3.14 for and round your answer up to the next foot)? There's a diagram of a right triangle hypotenuse labeled as 10___shorter leg labeled as 6..bottom leg is labeled 8ft. Inside the triangle is a circle with a diameter of 4ft PLEASE HELP ME.
area of triangle: 1/2 * 6 * 8 = 24
area of circle: pi * 2^2 = 4pi
area of sod: 24 - 4pi = 11.43
To find the area of the triangular patch of grass, we need to first calculate the area of the triangle and then subtract the area of the circle.
1. Calculate the area of the triangle:
The triangle can be divided into two smaller right-angled triangles. We can use the formula for the area of a triangle: A = (base * height) / 2.
In this case, the two right-angled triangles have the following dimensions:
Triangle 1:
Base = 8 ft
Height = 6 ft
Triangle 2:
Base = 10 ft
Height = 8 ft
Area of Triangle 1 = (8 * 6) / 2 = 24 sq ft
Area of Triangle 2 = (10 * 8) / 2 = 40 sq ft
The total area of the triangular patch of grass is the sum of the areas of both triangles:
Total area = Area of Triangle 1 + Area of Triangle 2 = 24 sq ft + 40 sq ft = 64 sq ft.
2. Calculate the area of the circle:
To find the area of a circle, we use the formula A = π * r^2, where π is approximately 3.14 and r is the radius of the circle. In this case, the diameter of the circle is given as 4 ft, so the radius is half of that, which is 2 ft.
Area of the circle = π * (radius)^2 = 3.14 * 2^2 = 12.56 sq ft.
3. Calculate the area of the sod needed:
To find the area of the sod needed to complete the garden, we need to subtract the area of the circle from the total area of the triangular patch of grass.
Area of sod needed = Total area - Area of the circle = 64 sq ft - 12.56 sq ft = 51.44 sq ft.
Rounding up to the nearest foot, Jackson will need approximately 52 square feet of sod to complete the garden.