Question

Find the area of shaded region in the given figure​

Answer 1

To find:-

• Area of shaded region.

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Solution:-

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✤ ABCD is a square (beacuse it's all sides are equal) which is inside parallelogram AECF.

✤ AECF is parallelogram (beacuse AB is parallel to DC which are producing line AE and FC. Therefore, AE is also parallel to CF. Hence, Proved that AECF is parallelogram).

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In parallelogram AECF

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Area of parallelogram = Base × height

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Base = FC = 15 + 3 = 18 cm

Height = AD = 15 cm (∵ AD is measurement between two parallel lines AE and FC)

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Put the values,

$\implies \tt \: 18 \times 15$

$\implies \tt \:270$

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☄ Area of parallelogram is 270 cm²

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In square ABCD

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Area of square = Side × side

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Side = 15 cm

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Put the side in formula

$\implies \tt \: 15 \times 15$

$\implies \tt \: 225$

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Area of ABCD is 225 cm²

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Area of shaded region = Area of parallelogram - Area of square

$\implies \tt \:270 - 225$

$\implies \tt \:45$

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☀ Thus, Area of shaded region is 45 cm².

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More information:-

1. Parallelogram:-

• It's both Pair of opposite sides are equal and parallel.
• It's diagonal bisect each other.
• Perimeter of parallelogram is sum of all sides.
• Area of parallelogram is base × height.

2. Square:-

• It's all sides are equal and parallel.
• It's all angles are of 90°.
• Perimeter of square is 4 × side.
• Area of square is side × side.

Points to remember:-

• We always use square in unit (like meter , centimeter etc ) of area but in case of Perimeter we didn't use any square or cube in its unit we directly write centimeter , meter..etc.

☠ Always write unit after answer. If it is given in question beacuse if we forget to write It result in decrement in our marks.