Practice (54)
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle?
Rhombus $ABCD$ is similar to rhombus $BFDE$. The area of rhombus $ABCD$ is $24$ and $\angle BAD = 60^\circ$. What is the area of rhombus $BFDE$?
A circle of radius $2$ is centered at $O$. Square $OABC$ has side length $1$. Sides $AB$ and $CB$ are extended past $B$ to meet the circle at $D$ and $E$, respectively. What is the area of the shaded region in the figure, which is bounded by $BD$, $BE$, and the minor arc connecting $D$ and $E$?
In rectangle $ABCD$, we have $A=(6,-22)$, $B=(2006,178)$, $D=(8,y)$, for some integer $y$. What is the area of rectangle $ABCD$?
A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7 as shown. What is the area of the shaded quadrilateral?
A rectangle with a diagonal of length $x$ is twice as long as it is wide. What is the area of the rectangle?
In the figure, the length of side $AB$ of square $ABCD$ is $\sqrt{50}$ and $BE$=1. What is the area of the inner square $EFGH$?
The figure shown is called a trefoil and is constructed by drawing circular sectors about the sides of the congruent equilateral triangles. What is the area of a trefoil whose horizontal base has length $2$?
An equiangular octagon has four sides of length 1 and four sides of length $\frac{\sqrt{2}}{2}$, arranged so that no two consecutive sides have the same length. What is the area of the octagon?
In $ABC$ we have $AB = 25$, $BC = 39$, and $AC=42$. Points $D$ and $E$ are on $AB$ and $AC$ respectively, with $AD = 19$ and $AE = 14$. What is the ratio of the area of triangle $ADE$ to the area of the quadrilateral $BCED$?
A circle is inscribed in a square, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. What is the ratio of the area of the smaller circle to the area of the larger square?
An $8$-foot by $10$-foot floor is tiles with square tiles of size $1$ foot by $1$ foot. Each tile has a pattern consisting of four white quarter circles of radius $\frac{1}{2}$ foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?
Equilateral $\triangle ABC$ has side length $2$, $M$ is the midpoint of $\overline{AC}$, and $C$ is the midpoint of $\overline{BD}$. What is the area of $\triangle CDM$?
This figure consists of eight squares labeled A through H. The area of square F is16 units$^2$. The area of square B is 25 units$^2$. The area of square H is 25 units$^2$. In square units, what is the area of square D?
An optometrist has this logo on his storefront. The center circle has area 36\u03c0 $in^2$, and it is tangent to each crescent at its widest point (A and B). The shortest distance from A to the outer circle is $\frac{1}{3}$ the diameter of the smaller circle. What is the area of the larger circle? Express your answer in terms of \u03c0.
Quadrilateral ABCD is a square with BC = 12 cm. $\overset{\frown} {BOC}$ and $\overset{\frown} {DOC}$ are semicircles. what is the area of the shaded region?
In isosceles trapezoid $ABCD$, shown here, $AB = 4$ units and $CD = 10$ units. Points $E$ and $F$ are on $\overline{CD}$ with $\overline{BE}$ parallel to $\overline{AD}$ and $\overline{AF}$ parallel to $\overline{BC}$. $\overline{AF}$ and $\overline{BE}$ intersect at point $G$. What is the ratio of the area of triangle $EFG$ to the area of trapezoid $ABCD$? Express your answer as a common fraction.
In square units, what is the largest possible area a rectangle inscribed in the triangle shown here can have?
In rectangle ABCD, BC = 2AB. Points O and M are the midpoints of $\overline{AD}$ and $\overline{BC}$ , respectively. Point P bisects $\overline{AO}$ . If OB = $6\sqrt{2}$ units, what is the area of $\triangle{NOP}$?
A square of side length 1 inch is drawn with its center A on a circle O of radius 1 inch such that a side of the square is perpendicular to $\overline{OA}$ , as shown. What is the area of the shaded region? Express your answer as a decimal to the nearest hundredth.
Mr. Mayfeld is designing a sign for his ice cream shop. The sign will be a shape consisting of a semicircle and an isosceles triangle that he will paint to look like a cone with a scoop of ice cream. He will cut the figure out of a rectangular piece of plywood measuring 2 ft by 4 ft, as shown. The shaded regions will be cut away. If BE = 3BG and $\overline{AB}$ is parallel to $\overline{CE}$ , what is the total area of the resulting figure? Express your answer as a decimal to the nearest tenth.
In the figure shown here, the distance between any two horizontally or vertically adjacent dots is one unit. What is the area of the shaded polygon? Express your answer as a decimal to the nearest tenth.
A square is inscribed in a circle of radius 5 units. In each of the four regions bounded by a side of the square and the smaller circular arc joining the endpoints of that side, a square is drawn so that one side lies on the side of the larger square and the two opposite vertices lie on the circle, as shown. What is the total area of the five squares? Express your answer to the nearest whole number.
Let's name the coordinates of the vertices of a trapezoid are A(1, 7), B(1, 11), C(8, 4) and D(4, 4). What is the area of the trapezoid?
In trapezoid ABCD segments AB and CD are parallel. Point P is the intersection of diagonals AC and BD. The area of $\triangle{PAB}$ is 16 and $\triangle{PCD}$ is 25. We must find the area of the trapezoid.