Question

One of the diagonals of a quadrilateral is 20 cm in length and the lengths of perpendiculars on it from the opposite vertices are 8.5 cm and 12.5 cm. the area of the quadrilateral is​

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Answer 1

A N S W E R :

• Length of a diagonal = 20 cm
• Sum of perpendicular lengths = 8.5 cm and 12.5 cm

We have to find the area of quadrilateral.

★Let's find the area of given quadrilateral :

→ Area of quadrilateral = ½ × (Length of diagonal) × (Sum of perpendicular lengths)

→ Area of quadrilateral = ½ × 20 × (8.5 + 12.5)

→ Area of quadrilateral = ½ × 20 × 21

→ Area of quadrilateral = 10 × 21

→ Area of quadrilateral = 210 cm²

★ Types of Quadrilateral :

• Rectangle : Opposite sides are equal and parallel and also contains one right angle

• Rhombus : All sides are equal.The diagonals bisect each other.

• Square : All Sides are equal. Opposite sides are parallel and also contains one right angle.

Some formuals :

• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²

Answer 2

Given:-

• Length of Diagonal = 20cm
• Length of perpendiculars = 8.5cm and 12.5cm

Find:-

• Area of Quadrilateral.

Solution:-

we, know that

↦ Area of quadrilateral = 1/2 × (Length of Diagonal) × (Sum of lengths of perpendiculars)

↦ Area of quadrilateral = 1/2 × (d) × (a + b)

where,

• Diagonal, d = 20cm
• a = 8.5cm
• b = 12.5cm

• Substituting these values •

↬ Area of quadrilateral = 1/2 × (d) × (a + b)

↬ Area of quadrilateral = 1/2 × (20) × (8.5 + 12.5)

↬ Area of quadrilateral = 1/2 × (20) × (21)

↬ Area of quadrilateral = 1/2 × 420

↬ Area of quadrilateral = 420/2

↬ Area of quadrilateral = 210cm²

Hence, the area of the Quadrilateral is 210cm²