Question

Find the perimeter and area of a quadrilateral ABCD in which BC = 12 cm, CD = 9 cm, BD = 15cm, DA = 17 cm and ∠ ABD = 90°.

Answer 1

Consider △ ABD

Using the Pythagoras theorem

AD² = AB² + BD²

By substituting the values

17² =AB² + 15²

On further calculation

AB² = 289 – 225

By subtraction

AB² = 64

By taking out the square root

AB = √64

So we get

AB = 8cm

We know that

Perimeter of quadrilateral ABCD = AB + BC + CD + AD

By substituting the values

Perimeter = 8 + 12 + 9 + 17

By addition

Perimeter = 46cm

We know that area of △ ABD = ½ × b × h

It can be written as

Area of △ ABD = ½ × AB × BD

By substituting the values

Area of △ ABD = ½ × 8 × 15

On further calculation

Area of △ ABD = 60 cm²

Consider △ BCD

We know that BC = 12cm, CD = 9cm and BD = 15cm

It can be written as a = 12cm, b = 9cm and c = 15cm

So we get

So the area of quadrilateral ABCD = Area of △ ABD + Area of △ BCD

By substituting the values

Area of quadrilateral ABCD = 60 + 54 = 114 cm²

Therefore, the perimeter is 46cm and the area is 114 cm².