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)?
no dimensions given. no figures can be pasted here. Repost with some dimensions if you need help.
recall that the triangle has area bh/2 and the circle has area pi*r^2
To find out how many square feet of sod Jackson will need to complete the garden, we first need to calculate the area of the triangular patch of grass.
The triangular patch of grass is formed by the circle's radius and the two sides of the triangle. Since the circle's radius is not given, let's assume it as 'r'.
The area of a triangle can be calculated using the formula: A = (1/2) * base * height.
To find the base of the triangle, we need to calculate the circumference of the circle. The formula for the circumference of a circle is: C = 2 * π * r.
In this case, the circumference is given by the circle's boundary, which is the same as the perimeter of the triangle. The perimeter of the triangle is the sum of the lengths of all its sides.
Since we have a circular pond, the perimeter of the triangle is obtained by adding three times the radius of the circle to the three sides of the triangle.
Perimeter of the triangle = 3r + 2 * side length of triangle.
Let's say the side length of the triangle is 's'.
Now we have the perimeter of the triangle, we can calculate the base of the triangle using the formula: base = perimeter/3.
So, base = (3r + 2s)/3.
Once we have the base and the radius of the circle, we can calculate the height of the triangle using the formula: height = √((r^2) - ((1/3) * base)^2).
Now, we have the base and the height of the triangle. We can calculate its area using the formula: Area = (1/2) * base * height.
Finally, to find the total area of sod needed, we add the area of the circle (π * r^2) and the area of the triangle.
Adding the two areas together, we can get the total area of sod required for Jackson to complete the garden.
Note: Remember to round the final answer to the next foot as mentioned in the question.