Question:
A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as \(4\) cm, \(5\) cm and \(7\) cm. Then the area of land of the farmer in sq. cm is
A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as \(4\) cm, \(5\) cm and \(7\) cm. Then the area of land of the farmer in sq. cm is
Show Hint
For a triangle with sides \(a,b,c\), Heron's formula is
\[
\Delta=\sqrt{s(s-a)(s-b)(s-c)},
\]
where
\[
s=\frac{a+b+c}{2}.
\]
Updated On: Jun 24, 2026
- \(2\sqrt{6}\)
- \(4\sqrt{6}\)
- \(\sqrt{6}\)
- \(8\sqrt{6}\)
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The Correct Option is B
Solution and Explanation
Step 1: Use Heron's formula.
The sides of the triangle are \[ a=4,\quad b=5,\quad c=7 \] The semi-perimeter is \[ s=\frac{a+b+c}{2} \] \[ s=\frac{4+5+7}{2} \] \[ s=\frac{16}{2}=8 \]
Step 2: Apply Heron's formula.
Area of triangle is \[ \Delta=\sqrt{s(s-a)(s-b)(s-c)} \] Substituting the values, \[ \Delta=\sqrt{8(8-4)(8-5)(8-7)} \] \[ \Delta=\sqrt{8\cdot 4\cdot 3\cdot 1} \] \[ \Delta=\sqrt{96} \] \[ \Delta=\sqrt{16\cdot 6} \] \[ \Delta=4\sqrt{6} \]
Step 3: Final conclusion.
Therefore, the area of the triangular plot is \[ \boxed{4\sqrt{6}} \]
The sides of the triangle are \[ a=4,\quad b=5,\quad c=7 \] The semi-perimeter is \[ s=\frac{a+b+c}{2} \] \[ s=\frac{4+5+7}{2} \] \[ s=\frac{16}{2}=8 \]
Step 2: Apply Heron's formula.
Area of triangle is \[ \Delta=\sqrt{s(s-a)(s-b)(s-c)} \] Substituting the values, \[ \Delta=\sqrt{8(8-4)(8-5)(8-7)} \] \[ \Delta=\sqrt{8\cdot 4\cdot 3\cdot 1} \] \[ \Delta=\sqrt{96} \] \[ \Delta=\sqrt{16\cdot 6} \] \[ \Delta=4\sqrt{6} \]
Step 3: Final conclusion.
Therefore, the area of the triangular plot is \[ \boxed{4\sqrt{6}} \]
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