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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.

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User Dotmido
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1 Answer

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Answer:

height = 4.8 cm

area = 120 cm²

perimeter = 62 cm

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)= (29^2-6^2-25^2)/(-2(6)(25))


\implies cos(C)= (180)/(-300)=-(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)(-(3)/(5))=53.13010235... \textdegree

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


(6)/(sin(90))=(h)/(sin(53.13..))


\implies (6)/(1)=(h)/((4)/(5))


\implies 6 * (4)/(5)=h


\implies h=(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

A parallelogram has adjacent sides 25 cm and 6 cm . if one diagonal is 29 cm then-example-1
User Hassan Zaheer
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