Geography, 14.07.2019 15:00 Tyrant4life

Heron’s formula: area use the triangle pictured to calculate the following measurements. perimeter: p = units semiperimeter: s = units area: a ≈ square units

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Answer from: tess97

The Perimeter, semi-perimeter, and area of a triangle with measurements 8 by 10 by 12 are 30 units, 15 units and 40 units square respectively.

What is Heron's formula?

Heron's formula is used in geometry to calculate the area of a triangle with respect to its sides. The formula is as follows:

$\rm Area\:of\:triangle = \sqrt{s(s-a)(s-b)(s-c)}$ , where s is the semi-perimeter of the triangle and a, b, and c are the length of its sides.

The perimeter of a triangle is the boundary of the triangle calculated as the sum of length of its sides. The formula therefore to calculate the perimeter of a triangle is:

$\rm P = a + b + c$ , where P is the perimeter of a triangle having sides a, b, and c.

Semi-perimeter is half the perimeter of a triangle. Therefore,

$\rm s = \dfrac{P}{2}$ , where s is the semi-perimeter.

Calculation of the perimeter of the triangle with sides 8,10, and 12 units:

$\rm P = a + b + c\\\\\rm P = 8 + 10 + 12\\\\\rm P = 30 \:units$

Semi-perimeter of the triangle will be:

$\rm s = \dfrac{P}{2}\\\\\rm s = \dfrac{30}{2}\\\\\rm s = 15\:units$

The area of the triangle will be:

$\rm Area\:of\:triangle = \sqrt{s(s-a)(s-b)(s-c)}\\\\\rm Area\:of\:triangle = \sqrt{15(15-8)(15-10)(15-12)}\\\\\rm Area\:of\:triangle = \sqrt{15(7)(5)(3)}\\\\\rm Area\:of\:triangle = \sqrt{1575}\\\\\rm Area\:of\:triangle = 39.6862 \:units^2\\\\\rm Area\:of\:triangle =40 \:units^2\:(rounded)\\$

Therefore the perimeter is 30 units, semi-perimeter is 15 units and area is 40 units square.

Learn more about Heron's formula here:

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Answer from: arod20061

the complete question is

Heron’s formula: Area Use the triangle pictured to calculate the following measurements. Perimeter: p = units Semiperimeter: s = units Area: A ≈ square units. The triangle is 8 by 12 by 10

Part a) Calculate the Perimeter:

The perimeter of the triangle is the sum of its sides.

$P = 8 + 12 + 10\\ P=30 units$

the answer Part a) is

The perimeter is equal to 30 units

Part b) Calculate the Semi-perimeter:

The semiperimeter of a polygon is half its perimeter.

$s = P / 2\\ s=30/2\\ s=15 units$

the answer part b) is

the semiperimeter is equal to 15 units

Part c) Calculate the Area

we know that

You can calculate the area of a triangle if you know the lengths of all three sides, using a formula that
It is called "Heron's Formula"

$A = \sqrt{(s * (s-a) * (s-b) * (s-c))}$

where

s: is the semi-perimeter

a, b, c are the length sides.

$s=15 units\\ a=8 units\\ b=12 units\\ c=10 units$

$A = \sqrt{(15 * (15-8) * (15-12) * (15-10))}$

$A = \sqrt{(15 * (7) * (3) * (5))}$

$A = \sqrt{(15 * (105) )}$

$A = \sqrt{(1,575 )}$

$A= 39.7 units^{2}$

the answer Part c) is

$A= 39.7 units^{2}$

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