Question

Suppose a quadrilateral having a diagonal of length 10 cm, which divides the quadrilateral into two triangles and the heights of triangles with diagonals as the base, are 4 cm and 6 cm. Find the area of the quadrilateral.

Answer 1

Solution:

Given,

Diagonal, d = 10 cm

Height of one triangle, h1 = 4cm

Height of another triangle, h2 = 6cm

Area of quadrilateral = ½ d(h1+h2) = ½ x 10 x (4+6) = 5 x 10 = 50 sq.cm.

Answer 2

Area of quadrilateral ABCD= 50 cm².

Given:

• A quadrilateral having diagonal of length 10 cm, which divides the quadrilateral into two triangles and,
• The heights of triangles with diagonals as the base, are 4 cm and 6 cm.

To find:

• Find the area of the quadrilateral.

Solution:

Formula to be used:

Area of triangle= 1/2× base × height.

Step 1:

Refer the attachment; let the quadrilateral is ABCD.

In ∆ABD;

Base (BD)= 10 cm

Height (AL)= 4 cm

$Ar.(\triangle ABD) = \frac{1}{2} \times 10 \times 4$

or

$\bf Ar.(\triangle ABD) = 20 \: {cm}^{2 }$

Step 2:

In ∆BDC;

Base (BD)= 10 cm

Height (CM)= 6 cm

$Ar.(\triangle BDC) = \frac{1}{2} \times 10 \times 6$

or

$\bf Ar.(\triangle BDC) = 30 \: {cm}^{2}$

Step 3:

Area of quadrilateral ABCD: Ar.(∆ABD)+Ar.(∆BDC)

Area of quadrilateral ABCD= 20+30

Area of quadrilateral ABCD= 50 cm².

Thus,

Area of quadrilateral ABCD= 50 cm².

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