Geometry Questions

Team 2015 - EQUILATERAL TRIANGLE AREAS

1. (Team) The ratio of the height of a triangle ABC to the height of a triangle MNP is 2/9. If the two triangles are similar, what is the ratio of the area of the triangle ABC to the area of the triangle MNP? Give your answer as a common fraction.

2. (Sprint) How many square units are in the area of the largest triangle that can be inscribed in a circle whose area is 159 Pi? Round your answer to the nearest integer.

3. (Countdown) How many degrees are in the measure of the smaller angle that is formed by the hands of a clock when it is 4 o'clock?

4. (Sprint) The base of an isosceles triangle is 48 cm long. If the area of the triangle cannot exceed 1080 square centimeters, What is the maximum number of centimeters in the perimeter of the triangle?

5. Let ABCD be square with edge length of 5 cm. We draw a circle of center A and radius 5 cm. and a circle of center C and radius 5 cm.. What percent of the square is the area inside the square that is not inside the intersection of the two circles? Express your answer to the nearest whole number.

6. (Sprint) Let ABC be right triangle in C . Suppose that points D, E are on the side AB such that AC = CD = DE = EB . Suppose also that AE = 13 sqrt(3) in. What is the number of inches in DE ?

8. (Sprint) Let C be a circle of center O . Let A be a point on the circle. Let P be a point on the radius AO such that AP=9 cm, and PO=8 cm. From the point P we draw a perpendicular to the radius AO . This perpendicular intersects the circle on a point B . Find the length of BP .

9. (Target) A huge right pyramid whose square base measures 575 feet along each edge is sitting on its base on the ground. An ant is crawling on the pyramid along the shortest path from the ground to the vertex. When she reaches the vertex she is 421 feet above the base. To the nearest tenth of a foot, what is the positive difference she crawled and the height of the pyramid?

10. (Team) Find the number of degrees in the positive difference between the sum of the of the measures of the 14 interior angles having blue vertices and the sum of the of the measures of the 7 exterior angles having red vertices of the given polygon.

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