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Use the triangle pictured to calculate the following measurements. Then, calculate the area rounded to the nearest tenth using Heron’s formula.

Perimeter: p = units
Semiperimeter: s = units
Area: A ≈ square units

Use The Triangle Pictured To Calculate The Following Measurements Then Calculate The Area Rounded To The Nearest Tenth Using Herons Formula Perimeter P Units S class=

Sagot :

semsee45

Answer:

Perimeter: p = 30 units

Semiperimeter: s = 15 units

Area: A ≈ 39.7 square units

Step-by-step explanation:

Perimeter

The perimeter of a two-dimensional shape is the total distance around its outer edge.

Therefore, the perimeter (p) of the given triangle is the sum of its side lengths:

[tex]p=8+12+10 \\\\ p=30\; \sf units[/tex]

So, the perimeter of the triangle is:

[tex]\Large\boxed{\boxed{p=30\; \sf units}}[/tex]

[tex]\dotfill[/tex]

Semiperimeter

The semiperimeter is half the perimeter of a polygon.

Therefore, the semiperimeter (s) of the given triangle can be calculated by dividing its perimeter by 2:

[tex]s=\dfrac{p}{2} \\\\\\s=\dfrac{30}{2} \\\\\\ s=15\; \sf units[/tex]

So, the semiperimeter of the triangle is:

[tex]\Large\boxed{\boxed{s=15\; \sf units}}[/tex]

[tex]\dotfill[/tex]

Area

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

[tex]\boxed{\begin{array}{l}\underline{\textsf{Heron's Formula}}\\\\A=\sqrt{s(s-a)(s-b)(s-c)}\\\\\textsf{where:}\\ \phantom{ww}\bullet \;\textsf{$A$ is the area of the triangle.} \\ \phantom{ww}\bullet \;\textsf{$a, b$ and $c$ are the side lengths of the triangle.} \\ \phantom{ww}\bullet \;\textsf{$s$ is half the perimeter.}\end{array}}[/tex]

In this case:

  • a = 8
  • b = 12
  • c = 10
  • s = 15

Substitute the values into the formula and solve for A:

[tex]A=\sqrt{15(15-8)(15-12)(15-10)} \\\\ A=\sqrt{15(7)(3)(5)} \\\\ A=\sqrt{1575} \\\\ A=39.68626966596... \\\\A=39.7\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of the triangle is:

[tex]\Large\boxed{\boxed{A \approx 39.7\; \sf square\;units}}[/tex]

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