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ABCDE is a regular pentagon.

Quantity A

x

Quantity B

36




A thin metal plate in the shape of a parallelogram has an area of 80 square inches and is cut into two pieces using two cuts. Each cut is parallel to a side of the plate, as shown, and the ratio of the length of each cut to the length of the side of the plate to which the cut is parallel is 3 to 4. What is the area, in square inches, of the piece of the plate represented by the shaded region?


In square MNOP shown, the two shaded square regions have areas in the ratio 9 to 1. If square region MNOP has area 144, what is the area of each of the two unshaded rectangular regions?
If the degree measures of the three angles of a triangle are consecutive even integers, what is the measure of the smallest angle of the triangle?


$$AB < AD$$

Quantity A

$$x$$

Quantity B

$$y$$




x > y > 0

Quantity A

The area of the left triangle

Quantity B

The area of the right triangle




∠2 > ∠1 > ∠3 > ∠4

Quantity A

The length of BC

Quantity B

The length of AD




b=2a, c=3b

The exterior angle of which of the following angle is the greatest?
If the length of two sides of a triangle is 5 and 12, then which of the following could be the length of the third side?

Indicate all such possible values.
The perimeter of triangle A and B is 32 and 52, respectively

Quantity A

The area of triangle A

Quantity B

The area of triangle B


There is an isosceles triangle and an equilateral triangle with the same height.

Quantity A

The area of the isosceles triangle

Quantity B

The area of the equilateral triangle


The sum of the lengths of two sides of isosceles triangle T is 10, and T has a side of length 5.

Quantity A

The perimeter of T

Quantity B

15




AB=AC=AD,∠BAD=60°. What is the angle of ∠BCD?


In the figure shown, AB=BD=DC and the degree measure of angle ABD is 80.

Quantity A

The degree measure of angle DBC

Quantity B

30




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 consists of 3 semicircles and an equilateral triangle with sides of length 8. Each side of the triangle is a diameter of a semicircle.

Quantity A

The combined area of the 4 shaded regions

Quantity B

96




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?


The lower sides of the two equilateral triangles are parallel. If the side of the bigger equilateral triangle is 36, and the perimeters of the smaller equilateral triangle and the trapezoid beneath are the same, what is the side of the smaller equilateral triangle?

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