MathCounts Geometry Exercise – 1

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 $cm$.

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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 $cm^2$.