EQUILATERAL TRIANGLE

EQUILATERAL TRIANGLE

- is a triangle in which all three sides measures equal with each other.

Illustration:

Formula:

 

where:

A = Area

a = one side

Problem:

1. Find the area of a shape that has equal shape of a triangle with equal sides that measures 3 meters on one side.

Given:

a = 3 meters

Required: Area

Solution:

    = 

A = 1.71(3m) ² / 4 = 3.8475 sq. meters; final answer 

EQUILATERALTRIANGLE

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THE PERIMETER OF A TRIANGLE

THE PERIMETER OF A TRIANGLE:

Perimeter:

- the sum of all the sides of a closed plane figures.
- the boundary of a closed plane figure.

Perimeter of a triangle formula:

P = S1 + S2 + S3

Illustration:

where:

P = perimeter

S1 = side 1

S2 = side 2

S3 = side 3

Problem:

1. The triangular field has its sides measure 50 feet, 75 feet, and 100 feet as sides. Find the total length of the field. (note: you can use any of the side as side 1, 2, and 3).

Given:

S1 = 50 ft

S2 = 75 ft

S3 = 100 ft

Required: Perimeter

P = S1 + S2 + S3

P = 50ft + 75ft + 100ft

   = 225 ft.; final answer

2. Find the perimeter of a triangular-shaped object if one side measures 10 centimeters and the other two legs measures 8 centimeters each.

Given:

S1 = 10 cm.

S2 = 8 cm

S3 = 8 cm

Required: Perimeter

P = S1 + S2 + S3

P = 10 cm + 8 cm + 8 cm

   = 26 cm.; final answer

3. If a fence, in a right-triangular shaped ,  has longest side measure doubled by one of its side, what is the perimeter if such one side measures 4 meters?

Let:
 4 = one side
2(4) =  8 = longest side

Then one more side is unknown which phytagorean theorem can be the tool to find it.

 h² = a² + o²

^{where: h = hypotenuse side, a = adjacent side, o = opposite side}

^Then:

 h² = a² + o² 
 8² = 4² + o² 
64 = 16 + o²

64 - 16 = o²

^{sqrt. of 48 = o}

^0r

^{0 = 6.928}

^Thus:

Given:

S1 = 4 meters

S2 = 6.928 meters

S3 = 8 meters

Required: Perimeter

P = S1 + S2 + S3

P = 4 meters + 6.928 meters + 8 meters

   = 18.928 meters.; final answer

^{4. The perimeter of a triangle measures 100 feet. If the measure of two sides, S1 and S2, were 25 feet and 30 feet respectively, what is the measure of the other side?}

Given:

S1 = 25 feet

S2 = 30 feet

Perimeter = 100 feet

S3 = ?

Required: S3

From:

P = S1 + S2 + S3

then:

S3 = P - S1 - S2

     = 100 feet - 25 feet -30 feet

     = 45 feet; final answer

  

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AREA OF A TRIANGLE

AREA OF A TRIANGLE:

Illustration 1:

Illustration 2:

FORMULA: A = 1/2 b*h

Where:

A = area

b = base

h = height

Example:

1. Find the area of a triangle whose base is 4 feet long with the height of 5 feet.

Given:

base = b = 4 ft.

height = h = 5 ft.

Solution:

A = 1/2 b*h

   = 1/2 (4 ft. * 5 ft.)

   = 1/2 (20 ft ²⁾

   = 10 ft ^{2 , final answer}

2. A triangle has the base measures 20 inches and 15 inches for the height.What is the area of the triangle?

Given:

b = 20 in.

h = 15 in.

Solution:

A = 1/2 b*h

   = 1/2 (20 in. * 15 in.)

   = 1/2 (300 in ²⁾

   = 150 in ^{2 , final answer}

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