Respuesta :
Answer:
[tex]\text{Area of 1st plot}\approx 14.7\text{ yards}^2[/tex]
[tex]\text{Area of 2nd plot}\approx 8.9\text{ yards}^2[/tex]
1st plot encloses the larger area.
Step-by-step explanation:
We have been given the sides of two triangles. We are asked to find the area of given triangles using Heron's formula.
The area of a triangle with sides a, b and c would be:
[tex]\text{Area of }\Delta =\sqrt{S(S-a)(S-b)(S-c)}[/tex], where S is the semi-perimeter of triangle.
[tex]S=\frac{5+6+7}{2}=\frac{18}{2}=9[/tex]
Substitute given side lengths:
[tex]\text{Area of 1st plot}=\sqrt{9(9-5)(9-6)(9-7)}[/tex]
[tex]\text{Area of 1st plot}=\sqrt{9(4)(3)(2)}[/tex]
[tex]\text{Area of 1st plot}=\sqrt{216}[/tex]
[tex]\text{Area of 1st plot}=14.6969\approx 14.7[/tex]
Therefore, the area of 1st plot would be 14.7 square yards.
[tex]S=\frac{3+6+7}{2}=\frac{16}{2}=8[/tex]
Substitute given side lengths:
[tex]\text{Area of 2nd plot}=\sqrt{8(8-3)(8-6)(8-7)}[/tex]
[tex]\text{Area of 2nd plot}=\sqrt{8(5)(2)(1)}[/tex]
[tex]\text{Area of 2nd plot}=\sqrt{80}[/tex]
[tex]\text{Area of 2nd plot}=8.9442\approx 8.9[/tex]
Therefore, the area of 2nd plot would be 8.9 square yards.
Since area of first plot is greater than 2nd plot, therefore, 1st plot encloses the larger area.
