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in Parallelograms by (58.8k points)

Calculate the area of quad. ABCD, given in Fig.

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Best answer

Consider △ BCD

Using the Pythagoras theorem

We can write it as

DB2 + BC2 = DC2

By substituting the values

DB2 + 82 = 172

By subtraction

DB2 = 172 – 82

DB2 = 289 – 64

By subtraction

DB2 = 225

By taking the square root

DB = √ 225

So we get

DB = 15cm

We can find

Area of △ BCD = ½ × b × h

By substituting the values

Area of △ BCD = ½ × 8 × 15

On further calculation

Area of △ BCD = 60 cm2

Consider △ BAD

Using the Pythagoras theorem

We can write it as

DA2 + AB2 = DB2

By substituting the values

AB2 + 92 = 152

By subtraction

AB2 = 152 – 92

AB2 = 225 – 81

By subtraction

AB2 = 144

By taking the square root

AB = √ 144

So we get

AB = 12cm

We can find

Area of △ DAB = ½ × b × h

By substituting the values

Area of △ DAB = ½ × 9 × 12

On further calculation

Area of △ DAB = 54 cm2

So we get

Area of quadrilateral ABCD = area of △ DAB + area of △ BCD

By substituting the values

Area of quadrilateral ABCD = 54 + 60

By addition

Area of quadrilateral ABCD = 114 cm2

Therefore, the area of quadrilateral ABCD is 114 cm2.

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