Page 20 - Student Binder for AP Unit 1 Unit Circle_Neat

AP 1.8 Problem Solving for Pythagorean and

Special Triangles

1) In this problem, let's derive a formula for the area of an equilateral
triangle. Start with ABC, and equilateral triangle with side length of 4.
a. Let segment AX be an altitude of triangle ABC as shown. Find BX.
b. Find AX.
c. Determine the area of triangle ABC.

2) Draw triangle PQR as an equilateral triangle with side s. Using the
same principles as used in #1, find the area of PQR in terms of s.
3) New concept: Find the area of an isosceles triangle. Draw triangle JKM
where JK and KM each measure 5 units. For this problem, JM will
measure 8.
a. Rest your triangle using JM as a base.
b. Draw an altitude. What can you determine about the altitude and
base JM?
c. Find the measurement of the altitude.
d. What is the area of triangle JM?

5) What is the area of a regular hexagon with side measures 2 cm? (Hint:
a regular hexagon has 6 congruent angles and sides, and thus, consists
of 6 little equilateral triangles.)
6) What is the height of this stack of three congruent circles of radius 12
cm? (Hint: connect centers of circles to create equilateral triangles.)
7) What is the height of a stop sign (octagon) with sides of one foot long?
8) Riding your bicycle you roll over a piece of gum which sticks to the
bottom of your 24-inch diameter tire. Your roll forward and the tire

makes a 120 degree rotation . How high above the ground is the gum
on the tire?
9) Solve for unknown sides listed.

10) Pay attention to this one! It won't be the last time you see one like it. Wink.

11) Use the properties of kites to solve the area of this kite

Similar and Trig 12-13 Page 1