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Question

In a quadrilateral ABCD, AB = BC and CD = DA; AC and BD are diagonals such that AC = 6 cm and BD = 12 cm. What is the area of the quadrilateral?

This question was previously asked in
CDS 2 2024 Maths Question Paper (01-Sep-2024)
The correct answer is
36 square cm

Understanding the Quadrilateral Shape

The problem asks for the area of a quadrilateral ABCD where specific side lengths are equal: AB = BC and CD = DA. A quadrilateral with two distinct pairs of equal-length adjacent sides is known as a kite.

In this kite ABCD:

  • The pair of adjacent sides AB and BC are equal.
  • The pair of adjacent sides CD and DA are equal.

The diagonals provided are AC = 6 cm and BD = 12 cm.

Area Calculation for a Kite

The area of a kite can be calculated using the lengths of its diagonals. The formula for the area (A) of a kite is:

\( A = \frac{1}{2} \times d_1 \times d_2 \)

where \(d_1\) and \(d_2\) represent the lengths of the two diagonals.

Applying the Formula to Find the Area

We are given the lengths of the diagonals:

  • Diagonal \(d_1\) (AC) = 6 cm
  • Diagonal \(d_2\) (BD) = 12 cm

Now, we substitute these values into the area formula:

\( A = \frac{1}{2} \times AC \times BD \)

\( A = \frac{1}{2} \times 6 \text{ cm} \times 12 \text{ cm} \)

First, multiply the lengths of the diagonals:

\( 6 \text{ cm} \times 12 \text{ cm} = 72 \text{ square cm} \)

Then, multiply the result by \(\frac{1}{2}\):

\( A = \frac{1}{2} \times 72 \text{ square cm} \)

\( A = 36 \text{ square cm} \)

Final Area Result

The calculated area of the quadrilateral ABCD is 36 square cm.

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Similar Questions

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  2. In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If the diagonal BD = \(x\), then which one of the following is correct?

Important Questions from Quadrilaterals

  1. The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be

  2. The side of a rhombus is 26 cm. The length of one of its diagonals is 20 cm. The sum of the lengths of the diagonals of this rhombus is equal to the perimeter of a rectangle. If the difference between the length and breadth of the rectangle is 6 cm, then what is the area of the rectangle?

  3. PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:

  4. ABCD is a trapezium in which AB || DC and DC is perpendicular to BC. If ∠DAB = 110°, then ∠ABC - ∠ADC =_____.

  5. The adjacent angles of a rhombus are in the ratio of 3 : 6. The smallest angle of the rhombus is:

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