Playing with Constructions

In geometric art, repeating a shape at regular intervals creates a __________.

A line segment has __________ length.

If you are drawing a square with side $4\text{ cm}$, what tool is best for ensuring the corners are exactly $90^\circ$?

Which tool would you use to find the center of a pre-drawn circle?

If you use a compass to draw an arc from point $A$ and another arc with the same radius from point $B$, and these arcs intersect at point $C$, then the triangle $ABC$ is always:

To draw a ray $OX$ such that $\angle XOY = 45^\circ$, we can first construct a $90^\circ$ angle and then:

Which instrument is used to draw an angle of $108^\circ$ for a pentagon artwork?

In a construction, if arc $A$ and arc $B$ are drawn from centers $P$ and $Q$ respectively with the same radius $r$, and they intersect at two points, what must be true about the distance $PQ$?

When constructing an angle of $30^{\circ}$, which of the following is the final step?

If the diameter of a circle is $14$ cm, and a chord is drawn at a distance of $7$ cm from the center, what is the length of the chord?

A rectangle has a length of $12$ cm and a breadth of $3$ cm. Find its perimeter.

If the side of a square is doubled, how many times does its area increase?

Which property is common to both a square and a rectangle?

A square has a perimeter of $40$ cm. What is its area?

What is the cost of tiling a rectangular room $6$ m long and $4$ m wide at the rate of Rs $10$ per square metre?

A rectangle and a square have the same perimeter of $20$ cm. If the rectangle's length is $6$ cm, which figure has a larger area?

A square field has an area of $144$ m$^2$. A person runs around its boundary $3$ times. What is the total distance covered?

If the diagonal of a square is increased by a factor of $2$, by what factor does the area of the square increase?

A room is $12$ m long and $8$ m wide. It is to be floored with square tiles of $50$ cm side. If the cost of one tile is Rs $25$, find the total cost of flooring the room.

A square sheet of paper has an area of $144\text{ cm}^2$. From the four corners, four squares of side $2$ cm are cut off. What is the perimeter of the remaining shape?

In the construction of a square $ABCD$ where one side $AB = 5\text{ cm}$ is given, what must be the measure of $\angle ABC$ to ensure the figure is a square?

In the construction of a square, if the diagonal is $AC$, then angle $CAB$ is:

If you are given side $AB = 3\text{ cm}$ and $BC = 3\text{ cm}$ for a quadrilateral with $90^\circ$ angles, it is a:

What is the sum of the interior angles of a constructed square?

If a square and a rectangle have the same perimeter of $20\text{ cm}$, and the rectangle's length is $6\text{ cm}$, which has a larger area?

To construct a rectangle $ABCD$ where $AB = 5\text{ cm}$ and $BC = 12\text{ cm}$, what is the length of the diagonal $AC$?

If you construct a square on each side of a rectangle with sides $3\text{ cm}$ and $4\text{ cm}$, what is the total number of squares constructed?

A square $PQRS$ is constructed such that the distance between opposite midpoints of the sides is $14\text{ cm}$. What is the length of the diagonal $PR$ of this square?

A rectangle has a width of $w$ and a length of $w + 4$. If the diagonal is $20\text{ units}$ and the rectangle is to be constructed on a grid, which equation correctly represents the relationship used to find $w$?

When constructing a square using a compass, if you are given only the perimeter as $P$, the first step is to find the side length. If the perimeter is $P = 4(x + 3)$, what is the length of the side you would set your compass to?

Which of these figures is a special case of a rectangle where all sides are equal?

A wire of length $30\text{ cm}$ is bent to form a rectangle. If the width is $5\text{ cm}$, what is the length?

In the construction of a rectangle, what is the measure of each interior angle?

A rectangle is divided into two equal triangles by a diagonal. If the area of the rectangle is $50\text{ cm}^2$, what is the area of one triangle?

A rectangle is constructed using 12 small squares of area $1\text{ cm}^2$ each. Which of the following cannot be the perimeter of such a rectangle?

What happens to the perimeter of a rectangle if both its length and width are doubled?

A rectangular room is $5\text{ m}$ long and $4\text{ m}$ wide. If a square carpet of side $3\text{ m}$ is laid on the floor, find the area of the floor NOT covered by the carpet.

If the length of a rectangle is doubled and its width is halved, what happens to the area of the rectangle?

Find the cost of fencing a rectangular park of length $250\text{ m}$ and width $175\text{ m}$ at the rate of Rs $12$ per meter.

A rectangle is formed by joining two identical squares of side $s$ side-by-side. If the perimeter of the resulting rectangle is $30\text{ cm}$, find the side $s$ of the square.

In a square, the diagonals divide the square into four:

In a rectangle, the diagonals bisect each other. If the total length of one diagonal is $18\text{ cm}$, what is the length from a vertex to the intersection point?

In the figure of the square $ABCD$, what is the relationship between segments $AO$, $BO$, $CO$, and $DO$ if $O$ is the center?

If one diagonal of a square is $7\text{ cm}$, what is the length of the other diagonal?

In rectangle $ABCD$, diagonal $AC$ is $x + 10$ and $BD$ is $2x - 5$. What is the length of $AC$?

In square $ABCD$, if diagonal $AC = 14\text{ cm}$, find the area of the square.

Which construction property allows us to state that $\triangle ABC \cong \triangle ADC$ in rectangle $ABCD$ where $AC$ is a diagonal?

In a rectangle $WXYZ$, the diagonals $WY$ and $XZ$ intersect at $O$. If $WO = (2y + 3)$ and $OY = 11$, find the value of $y$.

If the diagonals of a quadrilateral are equal and bisect each other at $90^\circ$, the quadrilateral is most specifically a:

A rectangular plot has dimensions $8$ m by $6$ m. A wire is stretched along both diagonals to reinforce the fencing. What is the total length of the wire used for both diagonals?