Questions: A sector of a circle is shown below. Calculate the area of the shaded segment. Give your answer to 1 d.p. Not drawn accurately

Solution Steps

The area of a sector of a circle is given by the formula (θ/360) * πr², where θ is the angle of the sector in degrees and r is the radius. In this case, θ = 128° and r = 25 m. So, the area of the sector is (128/360) * π * 25² ≈ 701.62 m².

The area of the triangle formed by the two radii and the chord can be found using the formula (1/2) * ab * sin(C), where a and b are the lengths of two sides of the triangle, and C is the angle between those sides. In this case, a = b = 25 m (the radii), and C = 128°. So, the area of the triangle is (1/2) * 25 * 25 * sin(128°) ≈ 246.20 m².

The area of the segment is the difference between the area of the sector and the area of the triangle. Therefore, the area of the segment is 701.62 m² - 246.20 m² ≈ 455.42 m².

Final Answer: