ShmoopTube

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Here’s your shmoopy question du jour…

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The Scissors Bandit has escaped from prison

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and has been wreaking havoc, cutting shapes out of paper wherever he goes.

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The figure below consists of two identical square sheets of paper with a circle cut out

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of one and a triangle cut out of the other. 

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If one side of one of the squares measures 4 cm, find the area of the shaded region.

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If we work together, maybe we can bring this jerk to justice.

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And here are the potential answers...

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OK, so this question is testing our visualization skills…

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…as well as our ability to take “net” areas…

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…that is, we’ll get the areas of the squares and then subtract the areas of the shapes inside.

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Following in the Bandit’s footsteps, in a sense.

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The problem tells us that the sides here are each 4 centimeters.

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So we can get the areas of the squares pretty quickly.

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The formula is base times height… and boy do we use that formula a lot so be sure you know it cold.

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Each square’s area is 16 square centimeters.

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Now for the tricky part.

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We have to calculate the area of the triangle and the circle and SUBTRACT those areas from

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that of the square. Because we shmoop daily, we know the formulas

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for the area of a triangle and a circle – that is… one half base times height…

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…and pi r squared, respectively So… plugging in the triangle’s numbers

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we have one half times the base of 4 times the height of 4 and we get… 8 square centimeters.

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Then we do the same for the circle and we get pi times the quantity 2 squared or …4.

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Note that the radius is half the diameter of 4.

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So now we solve for the whole thing and we get the area of the squares, which is 32 MINUS

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the 8 from the triangle, MINUS the 4 pi from the circle.

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And that gives us 24 minus 4 pi or answer D.

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We’ve solved his crime… now it’s time for him to do the time…

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