MHB Find Area Problem in Multiple Choice Question

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SUMMARY

The discussion focuses on calculating the area of a shaded region in a geometry problem involving a square and a circle. The square has a side length of 10 cm, resulting in an area of 100 cm², while the circle, with a diameter of 10 cm, has an area of 25π/4 cm², approximately 19.63 cm². The blue shaded area is determined by subtracting the area of the circle from the area of the square, leading to a final result of approximately 21.5 cm². The calculations were confirmed by a participant named Serena.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically area calculations.
  • Familiarity with the formula for the area of a square: A = s².
  • Knowledge of the formula for the area of a circle: A = (1/4)πd².
  • Ability to perform arithmetic operations involving π (pi).
NEXT STEPS
  • Review the properties of geometric shapes, focusing on squares and circles.
  • Practice calculating areas of composite shapes involving subtraction of areas.
  • Explore the use of π in various mathematical contexts and its approximations.
  • Learn about advanced geometry topics, such as area under curves and integration.
USEFUL FOR

Students studying geometry, educators teaching area calculations, and anyone interested in solving mathematical problems involving shapes.

susanto3311
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hi all...

how to easy find to figure it out this problem..

how to find are that shading blue color..

please, see my picture..

thanks in advance...susanto3311
 

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    area problem.png
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Mathematics news on Phys.org
Hi susanto3311! :)

What is the area of a square with side 10?
And a circle with diameter 10?
 
I like Serena said:
Hi susanto3311! :)

What is the area of a square with side 10?
And a circle with diameter 10?

i don't understand what do you answer...
 
susanto3311 said:
i don't understand what do you answer...

The blue area is the area of the square minus the area of the circle.

A square with side $s$ has area $s^2$.
A circle with diameter $d$ has area $\frac 1 4 \pi d^2$.

What would you get if you calculate those?
 
I like Serena said:
The blue area is the area of the square minus the area of the circle.

A square with side $s$ has area $s^2$.
A circle with diameter $d$ has area $\frac 1 4 \pi d^2$.

What would you get if you calculate those?

hi Serena...

Finally, with your formula my calculation the result is 21.5 cm2.
it's true? please, corrected if my answer is wrong...

thanks Serena...
 

Attachments

  • blue answer.png
    blue answer.png
    1.5 KB · Views: 123
susanto3311 said:
hi Serena...

Finally, with your formula my calculation the result is 21.5 cm2.
it's true? please, corrected if my answer is wrong...

thanks Serena...

Yep. It's true. (Nod)
 

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