Circles
Triangles
Quadrilaterals
Polygons and Solids
Potpourri
100
A rectangle and semicircle are shown below. The area of the semicircle is 18*pi. If the unshaded area outside of the semicircle but inside the rectangle is 6*pi, what is the exact perimeter of the rectangle?
What is 24 + 4*pi?
100
ED is parallel to CA. Find the measure of ED
What is 16?
100
The 8 x 18 rectangle ABCD is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is y?
What is "6"?
100
Sydney drew a regular pentagon and a square that share a side, and then connected two pairs of vertices to form angle ∠ABC as shown below. What is the measurement of ∠ABC?
What is 450?
100
A triangle has side lengths 6, 8, 10. Midpoints of each side are connected to form another triangle. What is the perimeter of this second, smaller triangle?
What is 12?
200
Circles of diameter 1 inch and 3 inches have the same center. The smaller center is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue painted area to the red painted area?
What is "8"?
200
Find the area of the triangle below. Round to the nearest tenth.
What is 29.4?
200
An isosceles trapezoid has a base angle of 600. It's bases measure 6 and 10. Find the exact value of the area of the trapezoid.
16√3
200
Find the area of the blue region.
What is 53 units?
200
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 6 square units, what is the area of the hexagon?
What is 9 square units?
300
Sector OAB is a quarter of a circle of radius 3 cm. A circle is drawn inside this sector, tangent at three points as shown. What is the radius, in centimeters, of the inscribed circle? Express your answer in simplest radical form.
What is (3√2 - 3)?
300
All of the triangles in the diagram below are similar to isosceles triangle ABC, in which AB = AC. Each of the 7 smallest triangles has area 1, and triangle ABC as area 40. What is the area of trapezoid DBCE?
What is "24"?
300
The rectangle below has a special property: it can be dissected into two smaller, congruent, similar copies of itself. If the shorter side has a length of 1, what is the length of the longer side?
√2
300
A regular hexagon intersects two parallel lines, as shown below. Find the value of x.
What is 1710?
300
The midpoints of the sides of an equilateral triangle are connected to form a second triangle. A third triangle is formed by connecting the midpoints of the second triangle. This process is repeated until a twelfth triangle is formed. What is the ratio of the perimeter of the twelfth triangle to the perimeter of the fifth triangle?
What is 1:128?
400
A random point is selected within the larger circle below. If AC is the diameter of the large circle, and if the diameter of semicircle AB is half the diameter of semicircle BC, what is the probability that the point lies within the shaded region?
What is 1/3?
400
If AC=AB=3 and BC=2, find AD.
What is "7/3"?
400
In square ABCD, point M is the midpoint of side AB and point N is the midpoint of side BC. What is the ratio of the area of the triangle AMN to the area of the square ABCD? Express your answer as a common fraction.
What is "1/8"?
400
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut one half ft. from the top face. The second cut is one third ft. below the first cut, and the third cut is one-seventeenth ft. below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
What is 11 square feet?
400
In the figure below, the distance between adjacent dots in each row or column is 1 cm. Using these dots as vertices, how many triangles with an area of 3 square centimeters can be drawn?
What is 10?
500
Two tangent circles with radii of 9cm and 17 cm are placed inside a rectangle as shown below. Find the width of the rectangle given that its length is 50 cm.
What is 36 cm?
500
Triangle ABC is divided into triangular regions so that [ABX]=[ACY], as shown below.
If BX=12 and XC=XA=15, find the length of XY.
What is 3?
500
As shown in the figure, both ABCD and BEFG are squares. The shaded area is 10 square units. Find the area of ABCD.
What is 20 square units?
500
Some line segments are drawn inside a 6-by-12 rectangle, as shown below. Find the area of the purple region.
What is 24 square units?
500
Find the area of the quadrilateral below.
What is 50?