Find the area of the shaded region if JK = 3 ft (1 point)
The image is a circle with a radius 3 ft, and the angle made by points J,K and L equals 84 degrees. This makes up the shaded region of the circle.
To find the area of the shaded region, we first need to find the area of the sector (the portion of the circle formed by the angle) and then subtract the area of the triangle JKL.
1. Area of the sector:
The formula for the area of a sector of a circle is A = (θ/360)πr^2, where θ is the central angle in degrees and r is the radius.
Given that θ = 84 degrees and r = 3 ft, we can plug in these values to find the area of the sector:
A = (84/360)π(3)^2
A = (7/30)π(9)
A = (63/10)π
A ≈ 19.80 square feet
2. Area of triangle JKL:
To find the area of a triangle, we can use the formula A = 0.5bh, where b is the base and h is the height.
Since JK is the base and KL is the height, we have:
A = 0.5(3)(3)
A = 4.5 square feet
3. Subtract area of triangle from the area of the sector:
Shaded area = Area of sector - Area of triangle
Shaded area ≈ 19.80 - 4.5
Shaded area ≈ 15.30 square feet
Therefore, the area of the shaded region is approximately 15.30 square feet.