Calculating Area of Sector in Shaded Part of Diagram

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Homework Help Overview

The discussion revolves around calculating the area of a shaded region in a diagram, specifically involving the area of a sector and a triangle. The subject area includes geometry and trigonometry.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the area of the shaded part by subtracting the area of a triangle from the area of a sector. They express uncertainty about using trigonometry to find the area of the sector. Other participants suggest using the area formula for a circle and the fraction of the circle represented by the sector. Questions arise regarding the calculation of angle X and the validity of the triangle's area measurement.

Discussion Status

The discussion is active, with participants providing guidance on using the area formulas and trigonometric relationships. Multiple approaches to finding the angles and areas are being explored, but there is no explicit consensus on the area of the triangle or the method to find angle X.

Contextual Notes

There is a question regarding the accuracy of the area of the triangle being 27cm, which may affect the calculations. The original poster is also seeking clarification on the use of trigonometric functions in this context.

garyadamson
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I am trying to work out the area of the shaded part of the diagram. I've figured that If I was to work out the area of the triangle (27cm) and take it away from the sector, I'd have the area of the shaded bit.

I'm guessing that I'd have to use trigonometory to find the area of the sector, I really have no idea how to do this, and would appreciate some help. Thankyou
 
Last edited:
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You're on the right track.

You know the area of the entire circle; it's pi times the radius squared.

You also know what fraction of that area is included in the sector; it's x/360, where x is in degrees.

- Warren
 
Last edited:
Thanks for your help
But how would I work out the size of angle X. Would cos, sin or tan have to be used?
 
You know all three sides -- use the law of cosines to find the angles.

- Warren
 
Less elegantly, you can break the triangle into two congruent right-triangles... then apply trigonometry with a right-triangle.
 
Are you sure that the area of the triangle is 27cm?
 

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