Question

construct a quadrilateral DEAR with DE=6cm,EA=5cm,AR=5.5cm,RD=5.2cm and DA=10cm .Also find its area​

Answer 1

Step-by-step explanation:

sorry I only construct the quadrilateral but I don't find its area

Answer 2

The area of the quadrilateral DEAR is 21 cm².

Given:

DE=6cm

EA=5cm

AR=5.5cm

RD=5.2cm

DA=10cm

To Find:

Area of quadrilateral DEAR

Solution:

We are given the lengths of the sides of the quadrilateral DEAR.

DA is the diagonal of the quadrilateral DEAR, which divides the quadrilateral into two triangles, ΔDAR and ΔDAE.

So, the area of quadrilateral DEAR= area of ΔDAR + area of ΔDAE

Area of ΔDAR

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

Here, s represents the semi perimeter and a, b, and c are the sides of the triangle.

We know that, a= 10cm, b= 5.5cm, c= 5.2cm

$s=\frac{a+b+c}{2} =\frac{10+5.5+5.2}{2} =\frac{20.7}{2} = 10.35 cm$

Area of ΔDAR= $\sqrt{s(s-a)(s-b)(s-c)}$                    $=\sqrt{10.35(10.35-10)(10.35-5.5)(10.35-5.2)} =\sqrt{10.35 X 0.35 X4.85X5.15} \\=\sqrt{90.48} \\=9.51 cm^{2}$

Area of ΔDAE

We know that, a= 10cm, b= 5cm, c= 6cm

$s=\frac{a+b+c}{2} =\frac{10+5+6}{2} =\frac{21}{2} = 10.5 cm$

Area of ΔDAE= $\sqrt{s(s-a)(s-b)(s-c)}$  

$=\sqrt{10.5(10.5-10)(10.5-5)(10.5-6)} =\sqrt{10.5X0.5X5.5X4.5\\}}\\ =\sqrt{129.93} \\=11.39 cm^{2}$

So,

Area of quadrilateral DEAR= area of ΔDAR + area of ΔDAE

                                            = 9.51 cm² + 11.39 cm²

                                            = 20.9 cm² = 21 cm² (approx.)

Hence, the area of the quadrilateral DEAR is 21 cm².

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