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Quadrilateral ABCE is a square, and triangle CDE is equilateral. If the perimeter of pentagon ABCDE is 30, what is the area of pentagon ABCDE?


The figure above shows a ceramic tile in the shape of an equilateral triangle with sides of length 12 inches. Parts of the tile are gray, as represented by the shaded regions, and the rest of the tile is white. The equilateral triangle in the middle of the tile has sides of length 9 inches and consists of nine congruent equilateral triangles. What fraction of the area of the tile is gray?
Each side of a triangle has a length of 1

Quantity A: The area of the triangle

Quantity B: $$\sqrt{2}$$


The figure consists of 14 identical equilateral triangular regions. If the area of the figure is $$56\sqrt{3}$$ what is the total length of all the sides shown in the figure?


Quantity A

x

Quantity B

4


An isosceles triangle has sides of length x, 2x and 2x. If the area of the triangle is $$25\sqrt{15}$$, what is the value of x?
Point P lies inside rectangle ABCD so that PA=2, PB=3, and PC=4. What is the value of PD?


AB∥ED,△ABC and △EDC are similar triangles,and the area of △EDC equals to $$\frac{1}{9}$$ of the area of △ABC. What is the ratio of AE to EC?


The area of square region ABIH equals the area of square region JDEF. Quadrilateral BJFI is a parallelogram. The area of squared region ACEG is 9 times the area of square region ABIH.

Quantity A

The area of ABIH

Quantity B

The area of BJFI




In the trapezoid, line segment AB is parallel to GH and JI. If the overall altitude of the trapezoid is 20cm, and the distance between line segment AB and GH is x cm, then which of the following would be an expression, in terms of x, the length of line segment AB?
A metalworker has two sheets of metal. The first sheet is in the shape of an equilateral parallelogram with two opposite angles of measure 60 degrees each. The second sheet is in the shape of a square. If the metalworker cuts out the largest possible circle from each sheet, then the areas of the two circles will be equal. What is the ratio of the area of the first sheet to the area of the second sheet?


The figure shows a window that is in the shape of a rectangle with a semicircle at the top. The radius of the semicircle is x feet, and the perimeter of the window is 26 feet. What is the total area, in square feet, of the window in terms of x?


A certain closed curve consists of n semicircles having the same radius of $$\frac{r}{n}$$ together with a larger semicircle having a radius of r. The n semicircles are aligned along the diameter of the larger semicircle as indicated in the figure for n=7. The area of the region enclosed by the curve, in terms of n, and r, is which of the following?


As shown in the figure, the centers of the two circles are respectively on the circumference of each other, and the radius is 3. What is the perimeter of this figure?


The above two circles both have a radius of 5, and both pass through the center of the other circle.

Quantity A

The area of the shaded region

Quantity B

50π




In the xy-plane shown, the circle is centered at the origin. Line $$l$$ passes through the origin and the point (3, 4). Line $$m$$ is tangent to the circle at the point (3, 4). What is the the x-intercept of line $$m$$?

Give your answer as a fraction.
In Orange County, the number of acres available for development in 2000 was approximately what fraction of the total land area of the county? (1 square mile=640 acres)
Which of the following represents the number of square miles of land that was available for development in Seminole County in 2000? (1 acre=43,560 square feet and 1 mile = 5,280 feet)
In 2000, the population density in Lake County was x people per square mile, and the population density in Osceola County was y people per square mile. What was the population density, in people per square mile, for the two counties combined?


For the frequency distribution of the variable x shown in the table above, what is the median value of x?

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