MathFun4Kids

1. ________ In $\triangle{ABC}$, $D$ is the midpoint of $BC$. $E$ is on $AC$ so that $AE=2\ EC$. The area of $\triangle{ABC}$ is $60\ cm^2$. Find the area of $\triangle{ABF}$ in $cm^2$.

2. ________ The area of rectangle $ABCD$ is $36$. $E$ is on $AD$ so that $AE=3DE$. Find the area of the shaded region.

3. ________ In rectangle $ABCD$, $AB=8$, $AD=15$. The total area of the shaded regions is $70$. Find the area of quadrilateral $EFGO$.

4. ________ The area of square $ABCD$ is $120\ cm^2$. $E$ is the midpoint of $AB$, $F$ is the midpoint of $BC$. Find the area of quadrilateral $BGHF$ in $cm^2$.

5. ________ In $\triangle{ABC}$, $D$ is the midpoint of $AC$. $E$ and $F$ are on $BC$ so that $BE=EF=FC$. The area of $\triangle{ABC}$ is $30$. Find the area of quadrilateral $MNEF$.

6. ________ The area of rectangle $ABCD$ is $36\ cm^2$. The area of quadrilateral $PMON$ is $3\ cm^2$. Find the total area of shaded regions in $cm^2$.

7. ________ In parallelogram $ABCD$, $BC:CE=3:2$, $AD=15$. The area of $\triangle{ODE}$ is $6\ cm^2$. Find the area of the shaded region in $cm^2$.

8. ________ In trapezoid $ABCD$, $ABED$ is a parallelogram. The areas of three triangles are given. Find the area of the shaded region.

9. ________ In square $ABCD$, $AB=6$. $AE=\dfrac{1}{3}AC$, $CF=\dfrac{1}{3}BC$. Find the area the shaded region.

10. ________ Square $PQRS$ has 3 vertices on the 3 sides of $\triangle{ABC}$. $BQ=CQ$. Find the area of sqaure $PQRS$.

1. ________ The area of $\triangle{ABC}$ is $1$. $BD:DC=2:1$, and $E$ is the midpoint of $AC$. $AD$ intersects $BE$ at point $P$. Find the area of quadrilateral $PDCE$.

2. ________ Rectangle $ABCD$ is divided into 4 smaller regions, $K$, $L$, $M$, and $N$, with equal area. If the ratio of the length and the height of rectangular region $K$ is $\dfrac{3}{2}$, what is the ratio of the length and the height of rectangular region $N$? Express your answer as a common fraction.

3. ________ A rectangle metal sheet is cut into two circles and one smaller rectangle, as shown in shared regions, to form a cylinder-shaped oil container. Find the volume of the oil container in liters. Assume $\pi=3.14$, and round your answer to the nearest integer.

4. ________ $\triangle{ABC}$ is right and $AC=3$, $BC=4$, $AB=5$. Then $AC$ is folded to $AB$. Find the area of the shaded region, which is not overlapping with other parts of the original triangle.

5. ________ The area of the right $\triangle{ABC}$ is $12$. A semi-circle is drawn as shown. The area of the shaded region can be expressed as $a\pi-b$. Find the value of $a+b$.

6. ________ The area of rectangle $ABCD$ is $36\ cm^2$. $E$, $F$, and $G$ are midpoint of $AB$, $BC$, and $CD$ respectively. $H$ is on $AD$. Find the area of the shaded region in $cm^2$.

7. ________ The area of $\triangle{ABC}$ is $10\ cm^2$. $BA$ is extended to $D$ so that $DB=AB$. $CB$ is extended to $E$ so that $EA=2 AC$. $CB$ extended to $F$ so that $FB=3 BC$. Find the area of $\triangle{DEF}$ in $cm^2$.

8. ________ The area of square $ABCD$ is $900\ cm^2$. $E$ is the midpoint of $CD$. $F$ is the midpoint of $BC$. $BE$ intersects with $DF$ at $M$, with $AF$ at $N$. Find the area of $\triangle{MNF}$ in $cm^2$.

9. ________ $ABCD$ and $CGEF$ are two squares. $CF=3\ CH$. The area of $CHG$ is $6\ cm^2$. $E$ Find the area of pentagon $ABGEF$ in $cm^2$.

10. ________ In trapezoid $ABCD$, $AD\parallel BC$. $AD=BE=EC$. $BD$ intersects with $AC$ at $O$, and $AE$ at $P$. The area of $\triangle{AOD}$ is $10\ cm^2$. Find the area of quadrilateral $OPEC$ in $cm^2$.

1. ________ One rectangle is divided into four smaller rectangles. The areas of three smaller rectangles are $25\ cm^2$, $20\ cm^2$, and $30\ cm^2$ respectively, as shown in the diagram. Find the area of the shaded region (unit: $cm^{2}$)

3. ________ Two congruent right triangles overlap each other. $AB=8\ cm$, $BF=6\ cm$, and $EF$ is split into two segments, with the length of the top segment as $3\ cm$. Find the area of the shaded region in $cm^2$.

4. ________ Four congruent rectangles and one smaller square form a bigger square with its area as $144$. If the area of the smaller square is $4$, and $x$ and $y$ are the length and height of the rectangles, then $x=$________ and $y=$________.

5. ________ The area of $\triangle{EDF}$ is $6\ cm^{2}$ bigger than the area of $\triangle{ABE}$. The length and height of rectangle $ABCD$ are $6\ cm$ and $4\ cm$ respectively. Find the length of $DF$ in $cm$.

Preview in new tab(opens in a new tab)

6. ________ $\triangle{ABC}$ is divided by line $DE$ into two regions, one in black, one in white. If $BD=DC=4$, $BE=2$, $EA=4$, find the area ratio between the black region and the white region. Express your answer as a common fraction.

7. ________ The area of square $ABCD$ is $3\ cm^{2}$, $M$ is the midpoint of $AD$. Find the area of the shaded region in $cm^{2}$.

8. ________ 3 pieces of congruent square-shaped paper in color red, yellow, and green are placed in a box with a square-shaped bottom. They overlap with each other. If the visible areas of the red, yellow, and green paper are $20$, $14$, and $10$ respectively, find the area of the square-shaped bottom of the box.

9. ________ In trapezoid $ABCD$, $AD=3\ cm$, $BC=9\ cm$. The area of $\triangle{ABO}$ is $12\ cm^2$. Find the area of trapezoid $ABCD$ in $cm^2$.

10. ________ The side length of the larger square is $5\ cm$. The side length of the smaller square is $3\ cm$. Find the area of the shaded region in $cm^2$.