$5$ . Write an expression in square units that represents the area of the shaded segment of $\odot C$ . $\newline$ enVision'm Geometry - Assessment Resources

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5

. Write an expression in square units that represents the area of the shaded segment of

\odot C

\newline

enVision'm Geometry - Assessment Resources

Calculate Sector Area: To find the area of the shaded segment, we need to subtract the area of the triangle from the area of the sector of the circle.
Find Triangle Area: First, let's find the area of the sector. The formula for the area of a sector is $(\theta/360) \times \pi \times r^2$ , where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
Subtract Triangle from Sector: Assuming the central angle $\theta$ is given and the radius $r$ is known, plug these values into the formula to calculate the area of the sector.
Final Area Calculation: Next, we calculate the area of the triangle. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ . If the triangle is equilateral and the radius of the circle is the same as the side of the triangle, the height can be found using Pythagoras' theorem.
Final Area Calculation: Next, we calculate the area of the triangle. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ . If the triangle is equilateral and the radius of the circle is the same as the side of the triangle, the height can be found using Pythagoras' theorem.The height $(h)$ of an equilateral triangle can be found using the formula $h = (\sqrt{3}/2) \times \text{side}$ . Since the side is equal to the radius, we use $r$ for the side length.
Final Area Calculation: Next, we calculate the area of the triangle. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ . If the triangle is equilateral and the radius of the circle is the same as the side of the triangle, the height can be found using Pythagoras' theorem.The height $(h)$ of an equilateral triangle can be found using the formula $h = (\sqrt{3}/2) \times \text{side}$ . Since the side is equal to the radius, we use $r$ for the side length.Now, calculate the area of the triangle using the formula $\frac{1}{2} \times \text{base} \times \text{height}$ , where the base is $r$ and the height is $(\sqrt{3}/2) \times r$ .
Final Area Calculation: Next, we calculate the area of the triangle. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ . If the triangle is equilateral and the radius of the circle is the same as the side of the triangle, the height can be found using Pythagoras' theorem. The height $(h)$ of an equilateral triangle can be found using the formula $h = (\sqrt{3}/2) \times \text{side}$ . Since the side is equal to the radius, we use $r$ for the side length. Now, calculate the area of the triangle using the formula $\frac{1}{2} \times \text{base} \times \text{height}$ , where the base is $r$ and the height is $(\sqrt{3}/2) \times r$ . Subtract the area of the triangle from the area of the sector to find the area of the shaded segment.
Final Area Calculation: Next, we calculate the area of the triangle. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$ . If the triangle is equilateral and the radius of the circle is the same as the side of the triangle, the height can be found using Pythagoras' theorem. The height $(h)$ of an equilateral triangle can be found using the formula $h = (\sqrt{3}/2) \times \text{side}$ . Since the side is equal to the radius, we use $r$ for the side length. Now, calculate the area of the triangle using the formula $\frac{1}{2} \times \text{base} \times \text{height}$ , where the base is $r$ and the height is $(\sqrt{3}/2) \times r$ . Subtract the area of the triangle from the area of the sector to find the area of the shaded segment. Write the final expression for the area of the shaded segment, which is the area of the sector minus the area of the triangle.