Answer:
The area of the shaded region is to 3. significant figures
Step-by-step explanation:
Step one: find the two diagonals of the kite.
<em>The Horizontal diagonal can be obtained using the cosine rule:</em>
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<em>The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:</em>
Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.
This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.
Step two: Use the dimensions of the two diagonals of the Kite to find the area:
The area of a Kite is obtained using this formula:
, where p and q are the two diagonals.
hence,
Step three: Calculate the area of the sector of the circle.
Area of the sector is obtained using this formula
Step Four: Subtract the area of the sector from the area of the kite:
Area of the shaded region will be
This will be to 3. significant figures