AREA OF A SQUARE

AREA OF A SQUARE

Area of a square is the product of its two sides.

Illustration:

Formula for area of a square:

A = side x side

or

A = s²

^Where:

^{A = Area}

^{side(s) = side}

^Problem:

^{1. Find the area of a square whose side is 5 meters.}

^Given:

^{s = 5 m}

^{Required: Area}

^Solution: 

A = s²

A = (5m)²

A = 25 m² 

^{2. A rectangular bin has a base measured 3 feet on one side. What is the area of the base of a rectangular bin?}

^Given:

^{s = 3 ft}

^{Required: Area}

^Solution: 

A = s²

A = (3 ft)²

A = 9 ft² 

^{3. The diagonal of a square measures 36 feet. Find the area of this square.}

^{In this case the diagonal of a square is 36. Applying the Phytagorean theorem, we can say that one side of the square is 6 feet. Hence.}

^Given:

^{s = 6 ft}

^{Required: Area}

^Solution: 

A = s²

A = (6 ft)²

A = 36 ft^{2 ,} 

^{Please leave a comment on the comment box below. Thank you.}

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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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VOLUME OF A CUBE

VOLUME OF A CUBE

DEFINITION:

Volume - the amount of space occupied by a three-dimensional object as measured in cubic units.

Illustration:

Formula:

V = S * S * S = S³

where:

S = side

Problems:

1. Find the volume of a cube whose side measures 2 meters.

Given:

S = 2 meters.

Required: Volume

Solution:

V = S * S * S = S³
     = 2 m * 2 m * 2 m

    = 8 cubic meters; final answer

2. What is the volume of a cube whose one side measures 3 feet?

Given:

S = 3 ft..

Required: Volume

Solution:

V = S * S * S = S³

   =3 ft. 3 ft. 3 ft. 

    = 27 cubic feet; final answer

3.The side of a cube has a measure of 4 inches. What is its dimension?

Given:

S = 4 in.

Required: Volume

Solution:

V = S * S * S = S³

   = 4 in. * 4 in. * 4 in. 

    = 64 cubic inch; final answer

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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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PERIMETER OF A SQUARE

PERIMETER OF A SQUARE

Perimeter - the sum of all sides.

               - measure of distance around a closed plane figure.

Illustration:

Formula for the perimeter of a square:

P = S₁ + S₂ + S₃  + S_{4 =}  4S

where:

P = perimeter

s = side 

(note : S₁ = S₂ = S₃  = S₄₎

Problem:

1. Find the total perimeter of a frame in square shape having measure 10 inches in one side.

Given:

s = 10 in.

Required: Perimeter

Solution:

P = S₁ + S₂ + S₃  + S_{4 =}  4S

P = 10 in. + 10 in. + 10 in. + 10 in. = 4 * 10 in.

   = 40 in. ; final answer

1. The square -shaped fence has one side measures 100 feet. what is its perimeter?

Given:

s = 100 ft.

Required: Perimeter

Solution:

P = S₁ + S₂ + S₃  + S_{4 =}  4S

P = 100 ft. + 100 ft. + 100 ft. + 100 ft. = 4 * 100 ft..

   = 400 ft. ; final answer

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CIRCUMFERENCE OF A CIRCLE

CIRCUMFERENCE OF A CIRCLE

- it is the distance length of a circle around the circle.

Illustration:

Formula:

C = 2 πr      

or

C = πd 

where:

C = circumference

r = radius

d = diameter

π = pi = 3.1416

Problem:

1. Find the circumference of a circle whose radius is 4 inches.

Given:

r = 4 in.

Required: Circumference:

Solution: ( since the given is radius, it is better to use the formula C = 2 πr ).

Therefore from the formula C = 2 πr.

C = 2 πr

C = 2 *π* 4in.

C = 8 π in.; final answer

1. What is the circumference of a circle whose diameter measures 2 feet.

Given:

d = 2 ft.

Solution: ( since the given is diameter, it is better to use the formula C = πd ).

From the formula C = πd.

C = πd

C = π* 2ft.

C = 2 π ft.; final answer

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PRISM

PRISM

- a polyhedron of which two faces are equal polygons in parallel planes and the order faces are parallelograms.

Rectangular Prism:

- a prism whose six faces are rectangles.

Illustration:

Area Total or surface area: 

above:   A1 = l*w
bottom: A2 = l*w

4 SIDES: S1 = h*w
                S2 = h * w
                S3 = h * l
                S4 = h *  l

Area Total = A1 + A2 + S1 + S2 + S3 + S4

Problem:

1. The rectangular prism has the length measures 10 feet, width 8 feet, and stands 6 feet. Find the total surface area of the prism.

Given:

l = 10 ft.
w = 8 ft.
h = 6 ft.

Required: Surface area

Solution:

A1 = l*w = 10 ft* 8 ft = 80 square feet

A2 = l*w = 10 ft* 8 ft = 80 square feet

S1 = h*w = 6 ft * 8 ft = 48 square feet

S2 = h*w = 6 ft * 8 ft = 48 square feet

S3 = h*w = 6 ft *10 ft = 60 square feet

S4 = h*w = 6 ft *10 ft = 60 square feet

Area Total = A1 + A2 + S1 + S2 + S3 + S4
                 = 80 square feet + 80 square feet + 48 square feet + 48 square feet + 60 square feet + 60 square feet
                 = 376 square feet: final answer

2.  Find the total surface area of a prism with 5 centimeters by 5 centimeters by 5 centimeters as dimension.

Given:

l = 5 cm

w = 5 cm

h = 5 cm

Required: Surface area

Solution:

A1 = l*w = 5 cm* 5 cm = 25 square centimeters

A2 = l*w = 5 cm* 5 cm = 25 square centimeters

S1 = h*w = 5 cm* 5 cm = 25 square centimeters

S2 = h*w = 5 cm* 5 cm = 25 square centimeters

S3 = h*w = 5 cm* 5 cm = 25 square centimeters

S4 = h*w = 5 cm* 5 cm = 25 square centimeters

Area Total = A1 + A2 + S1 + S2 + S3 + S4

                 = 25 square centimeters + 25 square centimeters + 25 square centimeters + 25 square centimeters + 25 square centimeters + 25 square centimeters

                 = 150 square centimeters: final answer

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