a circle with a radius of 3cm sits inside a 8cm x7cm rectangle. what is the area of the shaded region?
1 answer:
Answer:
27.73 square centimeters
Step-by-step explanation:
<em>Assume the shaded region is the area outside the circle but inside the rectangle.</em>
<em />
Now, we need to find the area of rectangle and area of circle. Then we will subtract area of circle from area of rectangle to get our desired answer.
Area of Rectangle = length * width
Area of Rectangle = 8 * 7 = 56
Area of circle is given by the formula:
Area =
Where r is the radius, which is 3
So,
Area of Circle =
Thus, area of the shaded region is:
Area of Shaded Region = 56 - 28.27 = 27.73 square centimeters
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Answer:
Part a) The radii are segments AC and AD and the tangents are the segments CE and DE
Part b)
Step-by-step explanation:
Part a)
we know that
A <u>radius</u> is a line from any point on the circumference to the center of the circle
A <u>tangent</u> to a circle is a straight line which touches the circle at only one point. The tangent to a circle is perpendicular to the radius at the point of tangency.
In this problem
The radii are the segments AC and AD
The tangents are the segments CE and DE
Part b)
we know that
radius AC is perpendicular to the tangent CE
radius AD is perpendicular to the tangent DE
CE=DE
Triangle ACE is congruent with triangle ADE
Applying the Pythagoras Theorem
substitute the values and solve for CE
remember that
CE=DE
so