Question

A parallelogram has adjacent sides 25 cm and 6 cm . if one diagonal is 29 cm then find area , height corresponding to the sides 25 cm and perimeter.
very important question.....
plz do fast.​

Answer 1

Answer:

height = 4.8 cm

area = 120 cm²

perimeter = 62 cm

Step-by-step explanation:

**Please refer to the attached diagram when following the step-by-step**

First, find m∠C (green angle on diagram) by using the cosine rule:

$c^2=a^2+b^2-2abcos(C)$

$\implies 29^2=6^2+25^2-2(6)(25)cos(C)$

$\implies cos(C)= \frac{29^2-6^2-25^2}{-2(6)(25)}$

$\implies cos(C)= \frac{180}{-300}=-\frac{3}{5}$

$\implies cos(C)=126.8698976... \textdegree$

Therefore, the interior angle of the right triangle at point C (blue angle on diagram) is:

$180-cos^{-1}(-\frac{3}{5})=53.13010235... \textdegree$

Now use the Sine Rule (for finding sides) to determine height (h):

$\frac{6}{sin(90)}=\frac{h}{sin(53.13..)}$

$\implies \frac{6}{1}=\frac{h}{\frac{4}{5}}$

$\implies 6 \times \frac{4}{5}=h$

$\implies h=\frac{24}{5}=4.8$

So the height = 4.8 cm

Now we have determined the height, we can calculate the area by using the area of a parallelogram formula:

Area of a parallelogram = base x perpendicular height

⇒ area = 25 x 4.8 = 120 cm²

Parallelogram is a four-sided shape made up of two pairs of straight parallel lines that are equal in length.

Perimeter = sum of the sides

⇒ perimeter = 6 + 6 + 25 + 25 = 62 cm