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alisha [4.7K]
3 years ago
12

If the radius of circle A is 6 units, calculate the area of the shaded region...

Mathematics
1 answer:
meriva3 years ago
4 0

The formula of an area of a triangle:

A_{\triangle}=\dfrac{base\cdot height}{2}

We have:

\triangle_{FDE}:\ base=height=1\\\triangle_{GDH}:\ base=height=9

substitute:

A_{\triangle_{FDE}}=\dfrac{1\cdot1}{2}=0.5\\\\A_{\triangle_{GDH}}=\dfrac{9\cdot9}{2}=40.5

The formula of an area of a circle:

A_O=\pi r^2

We have r=6

Substitute:

A_O=\pi\cdot6^2=36\pi\approx36\cdot3.14=113.04

The area of the shaded region

A=A_O-(A_{\triangle_{FDE}}+A_{\triangle_{GDH}})\\\\A=113.04-(0.5+40.5)=113.04-41=72.04\ u^2

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Mathematical word describes both 27x and 6x in the expression 27x+6x?
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<h3>How to form mathematical expression from the given description?</h3>

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, the terms were 27x and 6x and the expression formed from them is 27x+6x

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