Math 310Math 310

Section 11.2Section 11.2

AreaArea

AreaArea

Area is measured using square units Area is measured using square units and the area of a region is the and the area of a region is the number of nonoverlapping square number of nonoverlapping square that covers the region.that covers the region.

ExEx

12 units squared

7 units squared

8 units squared

Finding AreaFinding Area

Formula’s for finding area:Formula’s for finding area: Area of a triangleArea of a triangle Area of a trapezoidArea of a trapezoid Area of a parallelogramArea of a parallelogram Area of a Area of a regularregular polygon polygon Area of a circleArea of a circle Area of a sectorArea of a sector

Area of a TriangleArea of a Triangle

The area of a triangle:The area of a triangle:

A = b· h/2A = b· h/2

where b is the base of the triangle and where b is the base of the triangle and h is the height.h is the height.

ExEx

b

h

If the base and height of the following triangle are 3 and 6, what is the area?

If the length of another side of the same triangle is 9, what must the altitude be with respect to that side?

Area of a TrapezoidArea of a Trapezoid

The area of a trapezoid:The area of a trapezoid:

A = (1/2)(bA = (1/2)(b11 + b + b22)· h)· h

where bwhere b11 and b and b22 are the bases (ie the are the bases (ie the parallel sides).parallel sides).

ExEx

h

b1

b2

If the bases of the trapezoid are 5 and 4 and the height is 3, what is the area?

Area of a ParallelogramArea of a Parallelogram

The area of a parallelogram:The area of a parallelogram:

A = b· hA = b· h

ExExIf the area of the following parallelogram is 18 units squared, and the height is half the base in length, then what are the base and height?

b

h

Regular Polygon TermsRegular Polygon Terms

DefDef

The apothem of a regular polygon is The apothem of a regular polygon is the segment from the center of the the segment from the center of the polygon to the midsegment of the polygon to the midsegment of the side.side.

ExEx

a

Area of Regular PolygonArea of Regular Polygon

The area of a regular polygon:The area of a regular polygon:

A = (1/2)· a· s· nA = (1/2)· a· s· n

where where nn is the number of sides of the is the number of sides of the polygon.polygon.

ExExThe following regular polygon has a side length of 3 and an apothem length of 5, what is the area?

a

s

Area of a CircleArea of a Circle

The area of a circle:The area of a circle:

A = A = ππ· r· r22

where where rr is the radius. is the radius.

ExEx

r

Find the area of the following circle if the radius is 7.

Area of a SectorArea of a Sector

The area of a sector of a circle:The area of a sector of a circle:

A = A = ππ· r· r22· (· (θθ/360)/360)

Where Where θθ is the angle of the sector. is the angle of the sector.

ExExFind the area of the sector of the circle if the radius is 1 and the arc is a 60° arc.

r

60°

Dimensional AnalysisDimensional Analysis

Again we can use the process of Again we can use the process of dimensional analysis to convert from dimensional analysis to convert from area in one unit to another. The area in one unit to another. The process is slightly longer now, process is slightly longer now, however, we don’t need to memorize however, we don’t need to memorize any new unit conversion tables.any new unit conversion tables.

ExEx

Convert 3 mConvert 3 m22 to mm to mm22.. Convert 6 ydConvert 6 yd22 to in to in22.. Convert 1 miConvert 1 mi22 to ft to ft22.. Convert 450000 cmConvert 450000 cm22 to km to km22

Convert 22 kmConvert 22 km22 to mi to mi22