Two adjacent side of a parallelogram are 74cm and 40cm one of its diagonals
is 102cm. Find area of the ||gram
please answer it..
Answers
Answer:
A parallelogram is formed of two congruent triangles;
Here each of the two triangles have sides of 74 cm, 40 cm and 102 cm.
For each triangle : 2s = 74+40+102 = 216, or s = 108.
By Heron’s equation: A = [108*(108–74)*(108–40)*(108–102)[^0.5
= [108*34*68*6]^0.5
= 1224 sq cm.
So, the area of the parallelogram is 2448 sq cm.
The distance between the longer parallel sides = 2448/74 = 33.08 cm and the distance between the shorter parallel sides = 2448/40 = 61.2 cm.
The acute angle of the parallelogram is (74x40/2)*sin theta = 1224
arc sin theta = 1224*2/(74*40) = 0,827027027 or theta = 55.8 deg and the obtuse angle = 124.2 deg
A diagonal of a parallelogram divides it two triangles of equal area.
So, use Heron's formula area of a triangle
√s(s-a)(s-b)(s-c)
In the present case, take a = 74, b= 40, c = 102. s=(a+b+c)/2.
Double that answer and you get the area of the given parallelogram.
Answer:
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