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Split the following shapes into rectangles and find the area of each. (The measures are given in centimeters)

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250cm 2

245 cm 2

246 cm 2

270cm 2

answer is B.

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Detailed Solution

The given figure is,
Question Image

We can split the figure into rectangles,
Question Image

By making lines BE and KH, split the given figure into three rectangles.
From the given figure,

Total area = area of square CDEB + area of square KJHI + area of rectangle AFGL

Area of square = length × breadth Area of rectangle = length × breadth

Area of square CDEB = BC×CD ⇒ 7×7 ⇒ 49cm 2

Area of square KJHI = KJ×JI ⇒ 7×7 ⇒ 49cm 2

Now,

BE=CD=7 cm

(opposite sides of the rectangle)
So,

A F = A B + B E + E F

(they are on one line)

A F = 7 + 7 + 7 ⇒ 21 c m

Area of rectangle AFGL=AF×GF ⇒ 21×7 ⇒ 147cm 2

So, the total area of the given figure is,
Total area = area of square CDEB + area of square KJHI + area of rectangle AFGL.
Substituting the values,

Total Area = 147+49+49 ⇒ 245 cm 2

Hence option (2) is correct.

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