Question

using herons formula
using herons formula, calculate the area of the
parallelogram to the nearest tenth of a square unit.
area ≈ square units

Explanation:

Step1: Calculate the semi - perimeter of the triangle

The sides of the triangle are \(a = 5\), \(b=8\), \(c = 11\).
The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{5+8 + 11}{2}=\frac{24}{2}=12\)

Step2: Apply Heron's formula to find the area of the triangle

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 12\), \(a = 5\), \(b = 8\), \(c = 11\) into the formula:
\(A=\sqrt{12(12 - 5)(12 - 8)(12 - 11)}=\sqrt{12\times7\times4\times1}=\sqrt{336}\approx18.3\)

Step3: Find the area of the parallelogram

Since the parallelogram is composed of two congruent triangles, the area of the parallelogram \(A_{p}=2A\)
\(A_{p}=2\times18.3 = 36.6\)

Answer:

\(36.6\)