6. Shiva has a piece of land, which is in the shape of a rhombus. He wants his two sons to work on the land
and produce different crops. He divides the land in two equal parts by drawing a diagonal. If its perimeter is
400 m and one of the diagonals is of length 120 m, how much area each of them will get?
Answers
Answer:
4800 m²
Step-by-step explanation:
Given that shiva divided the land, which is in the shape of a rhombus, in two equal parts. Since it is divided in two equal parts, it is likely that it would be divided by the diagonals. We will first find the side of land.
Perimeter of rhombus = 4 × side
→ 400 = 4 × side
→ side = 400/4
→ side = 100 m
Now since the land is to be divide via diagonals, it will be divided into two triangles of equal area, in which two sides would be side of rhombus and third side would be diagonal.
Area of triangle by Heron's formula =
where, s = semi perimeter of triangle and a, b and c are sides of the triangle.
s = (100 + 100 + 160)/2
s = 180 m
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