Question

in a parallelogram ABCD AB=13cm BC=14 AC=15 then aera of parallelogram. option (A) 54 cm square (B) 42 cm square (C) 168 cm square (D) 126 cm square​

Answer 1

AnswEr :

⋆ Reference of Image is in the Attachment :

• we will find the Area of Triangle ABC :

we will use Heron's Formula to find the Area.

⇒ s = $\sf\dfrac{a+b+c}{2}$

⇒ s = $\sf\dfrac{13+14+15}{2}$

⇒ s = $\sf\dfrac{42}{2}$

⇒ s = 21

$\boxed{ \sf Area = \sqrt{s(s - a)(s - b)(s - c)} }$

$\rightarrow\sf Area_{\tiny\triangle ABC }= \sqrt{s(s - a)(s - b)(s - c)}$

$\rightarrow\sf Area_{\tiny\triangle ABC }= \sqrt{21(21 - 13)(21 - 14)(21 - 15)}$

$\rightarrow\sf Area_{\tiny\triangle ABC }= \sqrt{21 \times8 \times 7 \times 6}$

$\rightarrow\sf Area_{\tiny\triangle ABC}= \sqrt{7 \times 3 \times2 \times 2 \times 2\times 7 \times 2 \times 3}$

$\rightarrow\sf Area_{\tiny\triangle ABC}=7 \times 3 \times 2 \times 2$

$\rightarrow \boxed{\sf Area_{\tiny\triangle ABC}=84 \: {cm}^{2}}$

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we know that the diagonal of Parallelogram divides in two congruent triangles :

⋆ Ar. of ΔADC = Ar. of ΔABC = 84 cm²

• we will calculate Area of Parallelogram :

⇝ Area of || ABCD = 2 × Area of ∆ABC

⇝ Area of || ABCD = 2 × 84 cm²

⇝ Area of || ABCD = 168 cm²

⠀

∴ Area of Parallelogram is [ C.] 168 cm²

Answer 2

Given :-----

• ABCD is a llgm .
• AB = 13cm
• BC = 14cm
• AC = 15cm

To Find :------

• Area of llgm ..

Formula used :----

• Since AC is diagonal of llgm .
• Area of ∆ABC = √s(s-a)(s-b)(s-c) by heron's formula , where s = semi-perimeter and a,b and c are sides of ∆ .
• area of llgm = 2×Area of ∆ABC (As diagonals of llgm divides it into two equal areas)

Calculation :----

Semi-Perimeter of ∆ ABC = (13+14+15)/2 = 42/2 = 21cm

Now, putting all values in Heron's Formula we get,,

$Area \: of \: \triangle \: ABC = \: \sqrt{21 \times (21 - 13)(21 - 14)(21 - 15)} \\ \\ Area\: \triangle \: ABC = \sqrt{21 \times 8 \times 7 \times 6} \\ \\ Area\: \triangle \: ABC = \sqrt{3 \times 7 \times 2 \times 4 \times 7 \times 2 \times 3} \\ \\ Area\: \triangle \: ABC = 3 \times 7 \times 2 \times 2 \\ \\ Area\: \triangle \: ABC = 84 \: {cm}^{2}$

Hence, Area of llgm = 2×84 = 168cm² (C)

(Hope it Helps you)

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Extra Brainly knowledge :-------

1) Opposite sides are parallel.

2) Opposite sides are congruent.

3) Opposite angles are congruent.

4) Consecutive angles are supplementary.

5) The diagonals bisect each other.