Multiple Choice
Which formula is used to find the area of a triangle when two sides and the included angle are known (SAS case)?
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7. Non-Right Triangles
Area of SAS & ASA Triangles
Multiple Choice
Given that the measure of central angle is radians in a circle of radius , what is the area of the shaded sector? Choose the correct formula from the options below.
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Verified step by step guidance1
Recall that the area of a sector of a circle is proportional to the measure of its central angle. The full circle has an angle of \(2\pi\) radians and an area of \(\pi r^{2}\).
To find the area of the sector with central angle \(\theta\), set up a ratio comparing the sector's angle to the full circle's angle: \(\frac{\theta}{2\pi}\).
Multiply this ratio by the total area of the circle to get the sector area: \(\text{Area of sector} = \frac{\theta}{2\pi} \times \pi r^{2}\).
Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\text{Area of sector} = \frac{\theta r^{2}}{2}\).
Thus, the formula for the area of the sector with central angle \(\theta\) radians and radius \(r\) is \(\frac{\theta \cdot r^{2}}{2}\).
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