[powerpoint] math - measuring area

7/29/2019 [Powerpoint] Math - Measuring Area

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Shapes to be discussed:

Rectangle

Square

Parallelogram

TriangleTrapezoid

Rhombus


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The formula of finding the rectanglesarea is simply multiplying itslength/width to the other.

A = L W

where A is the area while L is the

Length and W is the width.


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Example: A rectangle has a lengthof 3 centimeters and a width of 8centimeters. Find the area.

Solution: A = L W

= (3 cm) (8 cm)

= 24 cm2


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The formula in getting a squaresarea is by multiplying the side oredge of the square with its self.

A = S or

A = S Swhere A is the area and S is the side.


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Example: A square is said to have20 cm measured as its side. Find

the area

Solution: A = S

= 20 20 cm

= 400 cm


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Any parallelogram can betransformed into a rectangle. The

formula in finding the

parallelograms area is similar tothe rectangles with the height as

the length and base as the width.

A = Base x height orA = bh


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Example: The base of a certainparallelogram is 40 cm while the

height is 20 cm. Find the area.

Solution: A = bh

= (40 cm)(20 cm)

= 800 cm


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Any side of the triangle can be thebase. The height is theperpendicular distance between

the line containing the base andopposite verses.

A = x base x height or

= bh or

= bh or


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Example: A triangles basemeasures 12 cm. Its height

measures 10 cm. Find the area.

Solution: = x base x height= x 12 x 10 cm= x 120 cm= 120/2= 60 cm


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The formula of getting the area of acube is to multiply the area of aface by six.

SA = 6e


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Example: A cube has an edge of 10cm. Find the surface area.

Solution = SA = 6e= 6(10 cm)

= 6(100 cm)

=


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To get the surface area, :

SA = 2lw + 2hw + 2hl


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Example: A microwave oven has aheight of 18 inches, width of 18 inches

and length of 30 inches. Find the

surface area.

Solution = SA = 2lw + 2hw + 2hl= 2(30)(18)+2(18)(18)+2(18)(30)= 2(540) + 2(324) + 2(540)

= 1080 + 648 + 1080=


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The lateral area, L, of a right prism isgiven by

L = hp

=(height)(perimeter)


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Example : A prism has a height of 13cm and a perimeter of 24 cm.

Find the lateral area.

Solution = L = hp=(height)(perimeter)

=(13)(24)

=


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Example : A prism has a length of 24cm and a base of 43 cm. Find thelateral area.

Solution = SA= l x 2b

= 24 x 2(43)= 24 x 86

=


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The lateral area of a regularpyramid equals half the product

of the slant height of the pyramid

and the perimeter of its base.

LA = lp


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Example : A pyramid has a lengthof 10 cm. It has a perimeter of 20

cm. Find the lateral area.

Solution = LA = lp

= (10)(20)

= 200 cm


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The surface area of a right prism isgiven by

SA = l + 2b


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The surface area of a regularpyramid is the sum of its lateralarea and its bases area.

SA = LA + b= lp + b


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Find the lateral surface area of theregular pyramid with a length of200, a perimeter of 100 and a

base of 100.

Solution = SA = LA + B

= (200)(100) + 100= 20000 + 100

=


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The lateral area of a circular coneof radius equals half the product

of the circumference of its base

and the slant height (length) ofthe cone.

LA = 2rl


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Example : Figure A is a circularcone with 30 ft as the length and

a radius of 20. Find the LA.

Solution = LA = 2rl= (2)(3.14)(20)(30)= (2)(1884)

=

3768=


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The surface area of a right circular

cylinder with radius and height equalsthe sum of its lateral area and the

area of its bases.

SA = LA + 2B = 2rh + 2r


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Example : An ice cream cone has alength of 12 cm and a radius of 2

cm. Find the surface area.

SA = rl + r

= (2)(12) + (9)

=288 ft.


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The lateral area of a right circularcylinder with radius equals the

product of the circumference of thebase and the height of the cylinder.

LA = 2rh


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Example : Find the a) LA and b) SA.

15 cm

26 cm


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a.) LA = 2 rh

= 2 (15) (26)= 780

=2449.2cm2

b.) SA = LA + 2B

= 780 + 2(225 )

= 780 + 450

= 1230

3962 2cm2

[powerpoint] math - measuring area

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