Question

The following exercise uses Heron's formula One triangular plot has sides 5 yards, 6 yards, and 7 yards. Another has sides 3 yards, 6 yards, and 7 yards. Find the area of each plot. (Round your answers to one decimal place.) first plot second plat Which plot endloses the larger area? first plot second plat

Answer 1

Answer:

$\text{Area of 1st plot}\approx 14.7\text{ yards}^2$

$\text{Area of 2nd plot}\approx 8.9\text{ yards}^2$

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:

$\text{Area of }\Delta =\sqrt{S(S-a)(S-b)(S-c)}$, where S is the semi-perimeter of triangle.

$S=\frac{5+6+7}{2}=\frac{18}{2}=9$

Substitute given side lengths:

$\text{Area of 1st plot}=\sqrt{9(9-5)(9-6)(9-7)}$

$\text{Area of 1st plot}=\sqrt{9(4)(3)(2)}$

$\text{Area of 1st plot}=\sqrt{216}$

$\text{Area of 1st plot}=14.6969\approx 14.7$

Therefore, the area of 1st plot would be 14.7 square yards.

$S=\frac{3+6+7}{2}=\frac{16}{2}=8$

Substitute given side lengths:

$\text{Area of 2nd plot}=\sqrt{8(8-3)(8-6)(8-7)}$

$\text{Area of 2nd plot}=\sqrt{8(5)(2)(1)}$

$\text{Area of 2nd plot}=\sqrt{80}$

$\text{Area of 2nd plot}=8.9442\approx 8.9$

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.