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# Ch 8 Geometry

### Ch 8 Terms and Conjectures

What is the formula for the area of a rectangle? A = bh
In a rectangle, parallelogram, rhombus, trapezoid, or triangle, what is perpendicular to the base (b)? the height (h)
What is the formula for the area of a parallelogram? A = bh
Does the height (aka altitude) of a parallelogram or triangle have to be contained within the polygon? No. Altitudes constructed from the acute vertices of an obtuse triangle are outside of the triangle. Altitudes constructed from an acute vertex of a parallelogram to the opposite side are outside of the parallelogram.
What is the formula for the area of a triangle? A = bh/2 OR A = (1/2)bh
What is the formula for the area of a trapezoid? A = ((base one + base two)*h)/2 OR A = (1/2)*(base one + base two)*h
What is the formula for the area of a kite? A = (1/2)*(diagonal one)*(diagonal two) OR A = (diagonal one)*(diagonal two)/2
What is the formula for the area of a regular polygon? A = (1/2)*asn OR A = (1/2)*aP
What is a perpendicular segment from the center of a regular polygon to one of the sides of the polygon? (The center of the polygon is also the center of the circle circumscribed around the polygon.) an apothem
What are the 6 congruent figures that a regular hexagon can be divided into? equilateral triangles
What are the 'n' congruent figures that any regular polygon can be divided into? isosceles triangles
What are the 5 congruent figures that a regular pentagon can be divided into? isosceles triangles
What is the formula for the area of one of the congruent isosceles triangles that any regular polygon can be divided into? A = (1/2)*as where a = apothem and s = side length
What is the formula for the area of a circle? A = (pi)*r^2
What is the formula for the circumference of a circle? C = 2*(pi)*r
Which answer is in terms of pi and simplified: (7(pi))/6) OR 1.17*(pi) (7(pi))/6)
Which answer is in terms of pi and simplified: 8(pi)+10(pi) OR 18(pi) 18(pi)
Which answer is in terms of pi and simplified: 2*(pi)*18 OR 36(pi) 36(pi)
Simplify this expression in terms of pi: 36(pi)+50 36(pi)+50
What is the formula for the area of a sector? A = (a/360)*((pi)r^2)
What is the formula for the area of a segment? A = (a/360)*((pi)r^2) - bh/2 Segment = Sector - Triangle
What is the formula for the area of an annulus? A = (pi)R^2 - (pi)r^2 Annulus area = area of large circle minus area of small circle
In the area formula for a sector, what is 'a'? Arc degree measure. It is the same measure as the central angle that intercepts it.
In the area formula for a regular polygon, what is 'a'? the apothem
What does a capital 'A' represent? Area
What does 'n' represent? number of sides
What does 's' represent? side length
What is surface area? The area of all of the faces or surfaces that enclose the solid figure. The area of all the figure's surface that could be exposed to air. Dents or holes in a solid figure both subtract and add to the surface area of the figure, with an overall addition
A prism's faces consist of two bases and 3 or more lateral faces. What kind of polygon are the lateral faces? The lateral faces of a prism are always rectangles or other parallelograms.
A pyramid's faces consist of one base and 3 or more lateral faces. What kind of polygon are the lateral faces? The lateral faces of a pyramid are always triangles.
What is always true about the bases of a prism? The bases of a prism are always congruent polygons.
What are the steps for finding surface area? 1) Draw a net and label the known lengths. 2) Find the area of each piece of the net. 3) Total the area of all pieces of the net.
What is a net? The 2 dimensional figure created by cutting along the edges of the solid, and laying each face or surface flat next to each other.
What is the formula for the surface area of a cylinder? SA = 2((pi)r^2)+2(pi)(r)(h) OR SA = 2(pi)(r)(r + h)
What is the formula for the surface area of a cone? (The capital 'L' is used to represent slant height in order to avoid confusion with the number 1.) SA = (pi)r^2+(pi)(r)(L) OR SA = (pi)(r)(r + L)
What is the formula for the surface area of a pyramid? (The capital 'L' is used to represent slant height in order to avoid confusion with the number 1.) SA = (1/2)asn + (1/2)sLn OR SA = (1/2)aP + (1/2)LP OR SA = (1/2)P(a + L)