Question

0.7- A Quadrilateral whose
side are 4 cm, 5 cm, 5 cm, 6 cm
and one of the diagonal is equal
to 6 cm. The area of
Quadrilateralis
O 19.17 sq cm
O 22.14 sq cm
O 21.12 sq cm
O 21.17 sq cm​

Answer 1

Answer:

Area of the quadrilateral is 23.31 cm²

Step-by-step explanation:

Given:

• A quadrialteral whose sides are 4 cm, 5cm, 5 cm, and 6 cm
• One of the diagonals = 6 cm

To Find:

• Area of the quadrilateral

Solution:

Here we have to find the area of the two triangles which is equal to the area of the quadrilateral.

We know by Heron's formula,

$\sf{Area\:of\:triangle=\sqrt{s(s-a)(s-b)(s-c)} }$

where s = semiperimeter and a,b,c are the sides of the quadrilateral.

Semiperimeter of first triangle = (4 + 6 + 6)/2

s of first triangle = 16/2 = 8

Now,

$\sf{Area\:of\:first\:triangle=\sqrt{8(8-4)(8-6)(8-6)}}$

Area of first triangle = √(8 × 2 × 4 × 2)

Area of first triangle = √128

Area of first triangle = 11.31 cm²

Now we have to find the area of the second triangle

Semiperimeter of second triangle = (5 + 6 + 5)/2 = 16/2

s of second triangle = 8 cm

Now,

$\sf{Area\:of\:second\:triangle=\sqrt{8(8-5)(8-6)(8-5)}}$

Area of second triangle = √(8 × 3 × 2 × 3)

Area of second triangle = √144

Area of second triangle = 12 cm²

Now,

Area of the quadrilateral = Area of first triangle + Area of second triangle

Substitute the data,

Area of the quadrilateral = 11.31 + 12

Area of the quadrilateral = 23.31 cm²

Hence area of the quadrilateral is 23.31 cm²