SPHERE

SPHERE

- a solid bounded by a closed surface every point of which is equidistant from a fixed point called the center.

Illustration:













Area of a Sphere:

A = 4 πr²

Where:

A = area

π = pi = constant = 3.1416

r = radius

Problem:

1. A spherical shape toy ball has the radius of 4 inches. Find the area of the said toy.

Given:

r = 4 in.

Required: Area:

Solution:

A = 4 πr²

    ^{= 4* π *( 4 in. )2}   

   ^{= 64π  in2} ; final answer

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PARALLELOGRAM

PARALLELOGRAM

- a quadrilateral in which both pairs of opposite sides are parallel.

Area = b * h

where:

b = base

h = height

Illustration of a parallelogram:

Problem:

1. A shape in the form of a parallelogram has 25 yard as base and 20 yard as height. Find the area of the said parallelogram.

Given:

b = 25 yd.
h = 20 yd

Required: Area

Solution:

Area = b * h
         = 25 yd. * 20 yd.
         = 50 square yard. ; final answer

2. A parallelogram-shaped object has 15 inches measure for the base and 10 inches for the height. What is the area of the parallelogram?

Given:

b = 15 in.

h = 10 in.

Required: Area

Solution:

Area = b * h

         = 15 in. * 10 in.

         = 150 square inches. ; final answer

3. What is the area of a parallelogram with the given dimension 2 inches for the width and 6 inches for the length.

Given:

b = 2 in.

h = 6 in.

Required: Area

Solution:

Area = b * h

         = 2 in. * 6 in 

         = 12 square inches. ; final answer

   

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TRAPEZOID

TRAPEZOID

THE AREA OF A TRAPEZOID

 A = (a + b) h / 2 ; ( just ignore c and d coz it will just follow the same result)













1. Find the area of a trapezoid that stands 6 meters whose top measures 5 meters and the bottom 11 meters.

Given: 

a = 5 m
b = 11 m
h = 6 m

Required: Area

Solution: ( substitute the values provided from the given)

 A = (a + b) h / 2 = (5 m + 11 m)( 6 m) / 2 = 48 sq. m. ; final answer

2. The height of a trapezoidal shape figure measures 10 inches with the base measures 12 inches and its top 9 inches. What is the area of the figure?

Given: 

a = 9 in

b = 12 in

h = 10 in

Required: Area

Solution: ( substitute the values provided from the given)

 A = (a + b) h / 2 = (9 in + 12 in)( 10 in) / 2 = 105 sq. in. ; final answer

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RECTANGLE

RECTANGLE

- a quadrilateral with four right angles.

Area of a rectangle:

Formula:

A = L * w

where: 

L = length
w = width

Illustration:

Example:

1.  The shape of a rectangular picture frame has the length of 12 inches and 8 inches as width. Find its area.

Given:

L = 12 in.
W = 8 in.

Required: Area

Solution:

A = L*W

    = 12 in.* 8 in.
    = 96 sq. in.; final answer

2. The rectangular fence measures 120 feet by length and 100 by with. Find the area of the fence.

Given:

l = 120 ft.

w = 100 ft.

Required: Area

Solution:

A = l*w

   = 120 ft * 100 ft.

   = 12,000 sq. ft.; final answer

3. A piece of land has one side measures 90 meters and the other side 100 meters. What is the area of the said land?

Given:

l = 100 m.

w = 90 m.

Required: Area

Solution:

A = l*w

   = 100 m.*  90 m

   = 9,000 sq. m.; 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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SQUARE

THE AREA OF A SQUARE:

A = a * a 

Where:

A = area

a = side of a square

Example:

1. Find the area of a square whose side measures 4 meters.

Given:

a = 4 m

Solution:

A = a * a

    = (4m)*(4m)

    = 16 sq. m. final answer

2. A table in square shape has 3 feet as measure on one side. Find the area of the table.

Given:

a = 3 ft.

Solution:

A = a * a

   = 3 ft. * 3ft

   = 9 ft. square; final answer

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