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Math 310

Math 310. Section 11.2 Area. Area. Area is measured using square units and the area of a region is the number of nonoverlapping square that covers the region. Ex. 12 units squared. 8 units squared. 7 units squared. Finding Area. Formula’s for finding area: Area of a triangle

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Math 310

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  1. Math 310 Section 11.2 Area

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

  3. Ex 12 units squared 8 units squared 7 units squared

  4. Finding Area Formula’s for finding area: • Area of a triangle • Area of a trapezoid • Area of a parallelogram • Area of a regular polygon • Area of a circle • Area of a sector

  5. Area of a Triangle The area of a triangle: A = b· h/2 where b is the base of the triangle and h is the height.

  6. h b Ex 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?

  7. Area of a Trapezoid The area of a trapezoid: A = (1/2)(b1 + b2)· h where b1 and b2 are the bases (ie the parallel sides).

  8. b1 h b2 Ex If the bases of the trapezoid are 5 and 4 and the height is 3, what is the area?

  9. Area of a Parallelogram The area of a parallelogram: A = b· h

  10. h b Ex If 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?

  11. Regular Polygon Terms Def The apothem of a regular polygon is the segment from the center of the polygon to the midsegment of the side.

  12. a Ex

  13. Area of Regular Polygon The area of a regular polygon: A = (1/2)· a· s· n where n is the number of sides of the polygon.

  14. a s Ex The following regular polygon has a side length of 3 and an apothem length of 5, what is the area?

  15. Area of a Circle The area of a circle: A = π· r2 where r is the radius.

  16. r Ex Find the area of the following circle if the radius is 7.

  17. Area of a Sector The area of a sector of a circle: A = π· r2· (θ/360) Where θ is the angle of the sector.

  18. r 60° Ex Find the area of the sector of the circle if the radius is 1 and the arc is a 60° arc.

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

  20. Ex • Convert 3 m2 to mm2. • Convert 6 yd2 to in2. • Convert 1 mi2 to ft2. • Convert 450000 cm2 to km2 • Convert 22 km2 to mi2

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