Area
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Key things to remember
o When finding the area of a triangle, you are taking 1/2 of the base x the height
o When finding the area of a parallelogram, you are multiplying the base x the height where height is
the altitude not the slanted side.
o Area of regular polygon = 1/2 of Perimeter x apothem
o When finding the apothem, do the following
 Angle = 360/(#of sides * 2)
 tan angle = 1/2 of side / apothem (i.e apothem = 1/2 of side/tan angle)
 Example: Pentagon with sides 8
 angle = 360/(5*2) = 36
 tan 36 = 4/apothem; apothem = 5.5
o Angles to keep in mind when dealing with regular polygons & apothems
 Pentagon – 36
 Hexagon – 30
 Heptagon – 25.7
 Octagon – 22.5
 Nonagon – 20
 Decagon – 18
ICA Hints
o YTMT: Area of Parallelogram
 #2: height is the leg of a 45-45-90 triangle.
o YTMT: Area of Sectors, Segments
 #3-6: area of sector - area of triangle
 #3 & #6: area of triangle = 1/2(r)(r)
 #4 &#5: area of triangle: use equilateral triangle formula
o YTMT: Area of Regular Polygons
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#1: use equilateral triangle formula
 #2: use square formula
 #3&#4: Use A = 1/2 Pa
 #5 & #6: need to use tan to find the apothem then use A = 1/2Pa
Homework Hints
o Circles, Sectors, Segments Worksheet (CSS)
 #3-6: multiply the area of the circle with the angle/360
 #7: dealing with right triangle
 #8-9: dealing with equilateral triangles.
o SG 11-3 WS
 pg623 #1: use equilateral triangle formula
 pg623 #2: use tan 36 = 5/apothem to find apothem
 pg623 #3: use square formula
 pg624 #1 & #4: subtract area of smaller circle from area of larger circle
Quiz Hints
o Quiz 1
 When finding area of triangle, use altitude and base
 When finding area of irregular figures, find area of each part and then add together
 12 questions: 3 triangles, 3 circles, 2 irregular shapes
o Quiz 2 (Regular)
 3 Irregular Shapes
 1 of each of the following shapes
 Trapezoid
 Kite
 Parallelogram (be sure to review 45-45-90 and 30-60-90)
 Square
 Triangle (Be sure to know all 3 triangle formulas. You never know which one will
be required)
 Regular Polygon
 Circumscribed square
 Area of segment (Hint: Area of sector – Area of triangle)
 2 ratio of sides & ratio of areas problems
 1 real-world application
 1 coordinate geometry problem (plot, determine type of quad and find its area)
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Quiz 2 (Honors/Magnet)
 3 Irregular Shapes
 1 of each of the following shapes
 Trapezoid
 Kite
 Parallelogram (be sure to review 45-45-90 and 30-60-90)
 Square
 Triangle (Be sure to know all 3 triangle formulas. You never know which one will
be required)
 Regular Polygon
 Circumscribed square
 Area of segment (Hint: Area of sector – Area of triangle)
 1 ratio of sides & ratio of areas problems
 1 real-world application
 1 coordinate geometry problem (plot, determine type of quad and find its area)
 Be able to derive the equilateral triangle formula from the formula of a triangle.
o Review Worksheet Part I
 #1a – use Pythagorean theorem to find the missing side then find the area of rectangle
 #1b – find the 30-side of 30-60-90 right triangle and then find the area of rectangle
 #4c – base is 7 and height is 10
 #14 – sides are all 13.
 #17b – missing parts of diagonals are 12 (Pythagorean triple)
Exam Hints
o Regular
 10 multiple choice
 5 true/false (be sure to specify why it is false
 6 problems dealing with squares/rectangles (be sure to review 1st 3 problems from Area
Review WS Part I)
 1 real-world application problem
 Be able to find area and perimeter of rhombus
 Be able to solve for apothem of regular polygon
 Be able to solve irregular shapes that include circles and semicircles
 Be able to find the area of a sector and a segment
o Honors/Magnet
 10 multiple choice
 5 true/false (be sure to specify why it is false
 2 real-world application problem
 Be able to find area and perimeter of rhombus
 Be able to solve for apothem of regular polygon
 Be able to solve irregular shapes that include circles and semicircles
 Be able to find the area of a sector and a segment
 Be able to find the area of a cyclic quadrilateral (hint: brahmagupta’s formula)
 Be able to derive any area formula from another area formula
 Be able to find area, perimeter, diagonal or side of a square when given any of the other
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Assessment 7 Study Guide Hints
o #2- Height is the 30 side of 30-60-90
o #19 – Apothem is 60 side of 30-60-90
o #23 – Faces/Bases are all triangles
Assessment 7 Exam Hints
o 26 multiple choice questions
 4 on area of triangle
 2 on area of parallelogram
 2 on area of trapezoid
 1 on area of rhombus
 1 on ratio of sides and ratio of areas
 2 on area of irregular shapes
 1 of each on area of circle, segment and sector
 1 on circle inscribed in square
 5 on identifying geometric solids
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4 on identifying edges, faces, vertices & bases & how many
 1 on net-view
 1 on lateral area of a prism