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

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.

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

, 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:

, where P is the perimeter of a triangle having sides a, b, and c.

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

, where s is the semi-perimeter.

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

Semi-perimeter of the triangle will be:

The area of the triangle will be:

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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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.

the answer Part a) is

The perimeter is equal to

Part b) Calculate the Semi-perimeter: 

The semiperimeter of a polygon is half its perimeter.

 the answer part b) is

the semiperimeter is equal to

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"

 where

 s: is the semi-perimeter

 a, b, c are the length sides.

the answer Part c) is

the answer is a the king was elected to his position