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Unformatted text preview: Math 131 FINAL EXAM Monday, May 14, 2007 Name: Lecture: W Page 2/9 Section 1: Midterm 1 Material 1. Explain what it means for two polygons to be similar. Give an example (include a picture). If two parallelograms‘ are similar, do their diagonals scale with the same ratio as their sides? 2. Give a Teacher’s Solution to the following problem. In the diagram below, ﬁnd 9:: M 1’ 1‘ .1 i w..w,..m»mm.—M«Wm Page 3/9 3. Two angles in a polygon are 80° and the rest are 20" larger. Find the number of sides of the
polygon. Draw a picture of the polygon. What kind of ploygon is it? Section 2: Midterm 2 Material 1. If the area of an equiiateral triangle is 4\/§, What is the height? Page 4/9 2. In a given parallelogram, the baSe is twice as long as the shorter side, and the height is 2 units.
If the larger interim angle of the parallelogram is 1350‘, ﬁnd the area of the parallelogram.
(In this problem, you will get an exact numerical answer.) 3. Prove: Given that the diagonals of a rhombus bisect each other, prove that they intersect
perpendicularly. Section 3 1. (a) What ratio do the sides of a (45—45—90) triangle satisfy? (b) Show why this is true. 2. In the ﬁgure below, ﬁnd B. {Gﬁ‘PJ’Eﬁ 1’ 5:. SEQ a Page 5/9 2"" '\‘£
:5. 1" GE; Page 6/9 3. A rectangular ﬁsh tank is 100cm long, 50cm wide, and 50cm tall. The water level is 400m.
After a new coral castle is added, the water level rose to 42cm. What is the volume in liters
of the castle? 4. (a) The area of a square is 400 cm2. Find the length of a side. (b) If the length is now increased by 15%, find the area of the new square. 0: Page 7/ 9 5. The diagram below shows a ﬂower bed formed by four quarter circles, each with radius 'r. ['1’ka _ 5 (a) Express the perimeter of the ﬂower bed in terms of r. (b) Show that the area of the ﬂoWer bed is given by A = (4 — 7r)'r2. (Be sure to draw the
picture that corresponds to the area.) Page 8/9 W (c) Assume the radius is 100 cm2. Using the approximation 77 R: 3.14, ﬁnd the area of the
ﬂower bed correct to one decimal place. (Express your answer in square meters.) 6. A right pyramid has a square base with sides 5 cm. If the height of the pyramid is 10 cm,
what is its volume? Page 9/9 7. Extra Credit Derive the formula for the surface area of a right circular cylinder. (Be sure
to include a diagram.) ' ...
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