How To Find Surface Area Of All Shapes

half-dozen.v: Expanse, Surface Area and Volume Formulas

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Area formulas

Let \(b\) = base

Permit \(h\) = tiptop

Let \(s\) = side

Allow \(r\) = radius

Table 6.v.one: Area formulas

Shape Proper noun	Shape	Surface area Formula
Rectangle		\(A=bh\)
Square		\(\begin{array}{l} A=b h \\ A=south^{2} \end{assortment}\)
Parallelogram		\(A=bh\)
Triangle		\(A=\dfrac{1}{2} b h\)
Circle		\(A=\pi r^{two}\)
Trapezoid		\(A=\dfrac{one}{2} h\left(b_{1}+b_{ii}\correct)\)

Surface Area Formulas

Variables:

\(SA\) = Area

\(B\) = surface area of the base of the figure

\(P\) = perimeter of the base of the effigy

\(h\) = height

\(s\) = camber tiptop

\(r\) = radius

Table 6.5.2: Surface Surface area formulas

Geometric Figure	Surface Area Formula	Area Meaning
	\(S A=ii B+P h\)	Find the area of each face. Add up all areas.
	\(South A=B+\dfrac{i}{two} s P\)	Find the area of each face. Add up all areas.
	\(South A=two B+ii \pi r h\)	Find the area of the base, times two, then add the areas to the areas of the rectangle, which is the circumference times the elevation.
	\(S A=4 \pi r^{ii}\)	Detect the area of the great circumvolve and multiply it past iv.
	\(S A=B+\pi r Southward\)	Discover the area of the base and add the product of the radius times the slant peak times PI.

Volume Formulas

Variables:

\(SA\) = Surface Area

\(B\) = area of the base of operations of the effigy

\(P\) = perimeter of the base of the effigy

\(h\) = height

\(due south\) = slant height

\(r\) = radius

Tabular array 6.5.3: Volume formulas

Geometric Figure	Book Formula	Volume Pregnant
	\(Five=B h\)	Find the surface area of the base and multiply information technology by the height
	\(V=\dfrac{1}{3} B h\)	Find the area of the base and multiply information technology by 1/three of the height.
	\(Five=B h\)	Find the area of the base and multiply information technology by the height.
	\(V=\dfrac{4}{3} \pi r^{3}\)	Notice the surface area of the slap-up circle and multiply it by the radius so multiply information technology by 4/3.
	\( V=\dfrac{1}{3} B h\)	Detect the area of the base and multiply it by 1/3 of the meridian.

Example \(\PageIndex{1}\)

Find the surface area of a circle with bore of 14 feet.

Figure six.five.1

Solution

\[\begin{aligned}A&=\pi r^{2}\\&=\pi(vii)^{two}\\&=49 \pi \text {anxiety}^{2}\\&=153.86 \text {feet}^{two} \end{aligned} \nonumber \]

Instance \(\PageIndex{two}\)

Notice the area of a trapezoid with a top of 12 inches, and bases of 24 and x inches.

Figure vi.5.two

Solution

\[\begin{aligned} A&=\dfrac{one}{two} h\left(b_{i}+b_{two}\right)\\ &=\dfrac{i}{2}(12)(24+10)\\ &=6(34)\\ &=204 \text { inches}^2 \cease{aligned}\nonumber \]

Case \(\PageIndex{iii}\)

Discover the surface area of a cone with a slant height of 8 cm and a radius of 3 cm.

Effigy half-dozen.v.3

Solution

\[\begin{aligned}
SA&= B+\pi rS\\ &=\left(\pi r^{2}\right)+\pi rs\\ &=\left(\pi\left(3^{ii}\right)\right)+\pi(iii)(eight) \\
&=ix \pi+24 \pi\\ &=33 \pi \text {cm}^{2}\\ &=103.62 \text {cm}^{two}
\terminate{aligned} \nonumber \]

Case \(\PageIndex{4}\)

Discover the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.

Effigy six.v.4

Solution

\[\begin{aligned}
SA&=B+\dfrac{1}{2} southward P\\
&=(b h)+\dfrac{ane}{2} south(2 b+two h) \\
&=(8)(12)+\dfrac{1}{ii}(10)(2(viii)+2(12)) \\
&=96+\dfrac{one}{2}(10)(xvi+24) \\
&=96+v(twoscore) \\
&=296 \text { yards}^{ii}
\stop{aligned} \nonumber \]

Example \(\PageIndex{5}\)

Find the volume of a sphere with a bore of 6 meters.

Effigy vi.5.5

Solution

\[\begin{aligned} V&=\dfrac{4}{iii} \pi r^{3}\\ &=\dfrac{4}{three} \pi(3)^{3}\\ &=\dfrac{4}{3}(27 \pi)\\ &=36 \pi \text { meters }^{iii}\\ &=113.04 \text { meters }^{3} \terminate{aligned} \nonumber \]

Partner Activity 1

1. Notice the surface area of a triangle with a base of operations of forty inches and a peak of 60 inches.
2. Observe the area of a square with a side of 15 feet.
3. Find the surface area of Earth, which has a diameter of 7917.5 miles. Use three.fourteen for PI.
4. Find the volume of a can a soup, which has a radius of 2 inches and a pinnacle of 3 inches. Employ three.xiv for PI.

Extension: Methods of Pedagogy Mathematics

Role 1

Assessments:

1. What is the Difference between Formative and Summative Assessments? Which One is More Important?
2. Formative Assessment Examples and When to Use Them
3. Summative Assessment Examples and When to Utilize Them

Part 2

Write a Formative and Summative Assessment for Your Lesson Programme

Part 3

Make certain you lot are working on Khan Academy throughout the semester.

Source: https://math.libretexts.org/Courses/College_of_the_Canyons/Math_130:_Math_for_Elementary_School_Teachers_%28Lagusker%29/06:_Geometry/6.05:_Area_Surface_Area_and_Volume_Formulas

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