The figure below shows the construction used to obtain a square with an area equal to that of a given rectangle.
ABCD is a rectangle, HDFG is a square, semicircle with center O
$$A ( ABCD ) = A ( HDFG )$$
The F vertex of the square HDFG in the figure lies on the semicircle with center O.
Given that the perimeter of rectangle ABCD is 36 cm, what is the diameter of the circle in cm?
A) 12
B) 15
C) 18
D) 21
E) 24

The following information is known about points A, B, C, D, and E in the plane.
$$\begin{aligned} & { [ A B ] \perp [ B C ] } \\ & { [ A B ] \cap [ C D ] = E } \\ & | A E | = | B C | = 4 \text { units } \\ & | A B | = | C D | = 7 \text { units } \end{aligned}$$
Given this, what is the length |DE| in units?
A) $\sqrt { 3 }$
B) $\sqrt { 5 }$
C) $\sqrt { 7 }$
D) 2
E) 3

ABCD is a square $\mathrm { AF } \perp \mathrm { FB }$ $\mathrm { DE } \perp \mathrm { AF }$ $| E F | = 4 \mathrm {~cm}$
Given that the area of triangle AFB in the figure is $30 \mathrm {~cm} ^ { 2 }$, what is the area of square ABCD in $\mathrm { cm } ^ { 2 }$?
A) 81
B) 100
C) 120
D) 136
E) 144

Teacher Aslı created the number 3 on a piece of paper by painting identical equilateral triangles inside an equilateral triangle ABC as shown in the figure.
If the area of equilateral triangle ABC is 96 square units, what is the painted area in square units?
A) 22 B) 27 C) 33 D) 36 E) 44

Given two squares as shown; the area of square ABCD is equal to 2 times the area of square CEFG.
Accordingly, what is the ratio $\frac { | \mathrm { AF } | } { | \mathrm { AG } | }$?
A) $\frac { \sqrt { 5 } } { 2 }$ B) $\frac { 2 \sqrt { 2 } } { 3 }$ C) $\frac { \sqrt { 10 } } { 3 }$ D) $\frac { 2 \sqrt { 2 } } { 5 }$ E) $\frac { \sqrt { 10 } } { 5 }$

A rectangle ABCD with short side 12 units and long side 18 units is folded along AL and KC such that $| \mathrm { KB } | = | \mathrm { LD } | = 4$ units. Then, with M and N being the midpoints of the sides they are on, this resulting shape is folded again along the line MN as shown to form a trapezoid.
Accordingly, what is the area of this trapezoid in square units?
A) 108 B) 105 C) 102 D) 99 E) 96

$$6 | \mathrm { AB } | = 3 | \mathrm { BC } | = 2 | \mathrm { CD } |$$
Above, three semicircles with diameters $[ \mathrm { AB } ] , [ \mathrm { BC } ]$ and $[ \mathrm { CD } ]$ with collinear centers are drawn inside a semicircle with diameter [AD], and the region between them is painted as shown in the figure.
If the perimeter of the painted region is $\mathbf { 24 \pi }$ units, what is its area in square units?
A) $44 \pi$ B) $48 \pi$ C) $52 \pi$ D) $56 \pi$ E) $60 \pi$

A square frame made by assembling four wires of equal length and fixed to the wall with nails at its corners as shown in Figure 1 covers an area of 100 square units on the wall.
As a result of the nails on corners A and B coming loose, one side slides down to form a rhombus shape as shown in Figure 2. In this frame, the height of corners A and B from the ground has decreased by 6 units each, while the position of the other two corners has not changed.
Accordingly, by how many square units has the area covered by the frame on the wall decreased?
A) 18 B) 20 C) 26 D) 30 E) 32

Identical boards in the shape of an isosceles trapezoid are joined together as shown in the figure to form a rectangular frame with a short side of 16 cm and a long side of 26 cm on the outside.
A picture is placed inside the frame of this frame such that the entire picture is visible and completely covers the inside of the frame. Accordingly, what is the area of this picture placed in $\mathbf { c m } ^ { \mathbf { 2 } }$?
A) 336
B) 312
C) 288
D) 264
E) 240

A point selected inside a pentagon is connected to the midpoints of the sides of the pentagon and to one vertex as shown in the figure. In this case, the regions formed are painted in different colors and the areas of these regions are written in square units on the figure.
According to this, what is the difference A - B?
A) 1
B) 1.5
C) 2
D) 2.5
E) 3

In a plane, three circles with radius r are constructed with the vertices of a right triangle $ABC$ as centers, and these circles do not intersect each other. The lengths of the parts on the sides of the triangle that are not inside these circles are given as 2 units, 3 units, and 5 units. Accordingly, what is the total area of the regions inside the circles but outside the triangle in square units?
A) $6 \pi$
B) $8 \pi$
C) $9 \pi$
D) $\frac { 9 \pi } { 2 }$
E) $\frac { 15 \pi } { 2 }$

In the figure, a semicircle with center A and radius $[AC]$ and a semicircle with center B and radius $[BC]$ are given. Point B is on the circle centered at A, and point A is on the circle centered at B.
Accordingly, what is the area of the shaded region in square units?
A) $36\pi$
B) $42\pi$
C) $48\pi$
D) $54\pi$
E) $60\pi$

Zeynep, who wants to prepare a cargo package, takes a right prism shaped cardboard box with a square base and a lid on its top surface as shown in Figure 1.
After placing what she wants to send in the box, Zeynep uses two blue colored bands, each with a width of 1 unit, to close the box. These two bands are parallel to the edges of the prism as shown in Figure 2, and each completely wraps around two side faces and the top face, excluding the bottom face. The total area covered by the bands on the surfaces of the prism is 25 square units.
Given that the total area of the outer surface of this box is 182 square units, what is the volume of the box in cubic units?
A) 100 B) 108 C) 147 D) 192 E) 196

An equilateral triangle with red-colored sides and an equilateral triangle with blue-colored sides are drawn such that one vertex of each is on a side of the other triangle, as shown in the figure.
In the resulting figure, the area of the yellow-colored triangle equals 4 times the area of the gray-colored triangle.
Accordingly, what is the ratio of the area of the triangle with red-colored sides to the area of the triangle with blue-colored sides?
A) $\frac{2}{3}$ B) $\frac{5}{6}$ C) $\frac{8}{9}$ D) $\frac{25}{27}$ E) $\frac{25}{36}$

In the figure, point $C$ is on the line segment $[AB]$, point $D$ is on the semicircle with diameter $[AB]$, and $m(\widehat{BAD}) = 18^{\circ}$.
In the figure, the area of the yellow-colored region equals 4 times the area of the blue-colored region. Accordingly, what is the ratio $\frac{|AC|}{|BC|}$?
A) $\frac{3}{2}$ B) $\frac{5}{3}$ C) $\frac{7}{4}$ D) $\frac{7}{5}$ E) $\frac{9}{5}$