Geometry and Measurement

A regular polygon with 3 sides is also known as a/an:

What is the exterior angle of a square?

Which statement is true for all parallelograms?

How many sides does a polygon have if the sum of its interior angles is $540^\circ$?

How many sides does a regular polygon have if the sum of its interior angles is $3240^\circ$?

What is the size of each interior angle of a regular polygon with $45$ sides?

A quadrilateral with all sides equal and no right angles is called a:

In an isosceles trapezoid, the diagonals are always:

A convex polygon has $n$ sides. If the sum of the interior angles is $S$, what is the sum of the interior angles of a polygon with $n + 3$ sides?

If each interior angle of a regular polygon is $165^{\circ}$, how many diagonals can be drawn from all vertices?

To draw a line segment exactly $5 \text{ cm}$ long using a ruler, you mark the start at $0$ and the end at:

If you construct a $60^\circ$ angle and its supplement, what is the measure of the supplement?

Which angle is formed by the intersection of the diagonals of a square?

What do we call a construction that splits an angle exactly in half?

The locus of points that are $2$ cm from a point $A$ AND $2$ cm from a point $B$ (where $AB = 3$ cm) consists of:

When constructing a triangle given $SAS$ ($Side_1=5$, $Angle=60^\circ$, $Side_2=7$), what is the third step after drawing $Side_1$ and the $60^\circ$ angle?

To construct a $165^\circ$ angle, one could bisect the angle between which two constructed angles?

If you construct a square with an area of $2$ square units, what is the length of its diagonal?

A median of a triangle connects a vertex to the midpoint of the opposite side. What is the locus of the midpoints of all segments drawn from a vertex $A$ to the opposite side $BC$?

In $\triangle ABC$, if the circumcenter and the incenter coincide, the triangle must be:

A large square with a side length of $5\text{ cm}$ has a small square of side $2\text{ cm}$ removed from its center. What is the area of the remaining shape?

A kite has diagonals measuring $22\text{ cm}$ and $10\text{ cm}$. Calculate its area.

A rhombus has diagonals of $1.5\text{ mm}$ and $4\text{ mm}$. What is the area?

A parallelogram has a base of $7\text{ m}$ and a height of $7\text{ m}$. What is its area?

A cross-shaped polygon is formed by a central square of side $6\text{ cm}$ and four identical trapeziums attached to each side. Each trapezium has parallel sides of $6\text{ cm}$ and $4\text{ cm}$ and a height of $3\text{ cm}$. What is the total area of the cross?

A rhombus has an area of $112\text{ cm}^2$ and one diagonal is $14\text{ cm}$. What is the length of the other diagonal?

A trapezium has parallel sides of $7\text{ cm}$ and $13\text{ cm}$. The height of the trapezium is equal to the average of its parallel sides. What is its area?

The area of a rhombus is $200\text{ cm}^2$. If one diagonal is $1/4$ of the other, find the length of the longer diagonal.

A trapezium has parallel sides $20\text{ cm}$ and $30\text{ cm}$. The non-parallel sides are $13\text{ cm}$ and $13\text{ cm}$. Find the area.

A rhombus has a side of $10\text{ cm}$ and one angle of $120^\circ$. Find its area.

What is the total surface area of a cube with a side length of $2.5 \text{ cm}$?

Find the total surface area of a cuboid that is $10 \text{ cm}$ by $1 \text{ cm}$ by $1 \text{ cm}$.

Calculate the volume of a cylinder with radius $1 \text{ cm}$ and height $20 \text{ cm}$ in terms of $\pi$.

What is the volume of a very small cube with a side length of $0.1 \text{ cm}$?

A cylinder has a volume of $448\pi\text{ cm}^3$ and a height of $7\text{ cm}$. Find its radius.

A cube has a volume of $1\text{ m}^3$. What is its surface area in $\text{cm}^2$?

A cuboid has a length of $12\text{ cm}$, a width of $4\text{ cm}$, and a height of $3\text{ cm}$. What is the length of the longest rod that can be placed inside the box?

A cuboid has a surface area of $52 \text{ cm}^2$ and its base is a square of side $2 \text{ cm}$. Find its volume.

If the volume of a cylinder is $125\pi \text{ cm}^3$ and its height is $5 \text{ cm}$, what is its curved surface area?

Find the ratio of the total surface area to the curved surface area of a cylinder with radius $r$ and height $h$.

What is the value of $c$ if $a=8$ and $b=6$ in a right triangle?

The hypotenuse of a right triangle is the:

If a triangle has sides $1.5$, $2$, and $2.5$, it is a right triangle. This is an application of:

Find the length of the diagonal of a rectangle with sides $7\text{ cm}$ and $24\text{ cm}$.

The side lengths of a triangle are $12, 13,$ and $5$. What type of triangle is it?

A rectangular park is $40\text{ m}$ long and $30\text{ m}$ wide. A path goes diagonally from one corner to the other. What is the length of the path?

In a coordinate plane, what is the distance from $(3, -4)$ to the origin $(0,0)$?

A spider is at one corner of a room with dimensions $3\text{ m} \times 4\text{ m} \times 5\text{ m}$. What is the distance to the opposite corner (the space diagonal)?

A triangle has side lengths $a = \sqrt{7}$, $b = \sqrt{18}$, and $c = 5$. Determine the type of triangle.

Calculate the area of a square whose diagonal is $\sqrt{50}\text{ cm}$.

If point $C(0, 0)$ is rotated $270^\circ$ clockwise, what are its new coordinates?

What is the order of rotational symmetry of a regular pentagon?

A point $(7, 3)$ is translated by the vector $\begin{pmatrix} -2 \\ 1 \end{pmatrix}$. The image is:

Reflect $(-3, -4)$ across the $y$-axis.

A point $(4, 4)$ is reflected across the line $y = x$ and then rotated $90^\circ$ counter-clockwise about the origin. What is the final image?

The point $(-2, 3)$ is mapped to $(6, 3)$ by a reflection. What is the line of reflection?

Point $(-4, -1)$ is rotated $270^\circ$ clockwise about the origin. What is the result?

The point $(2, 3)$ is translated by $\binom{1}{1}$, then reflected in the $y$-axis, then translated by $\binom{-1}{-1}$. What are the final coordinates?

A point $R(x, y)$ is rotated $180^\circ$ about the point $(a, b)$. The image is $R'(2a-x, 2b-y)$. If $R = (3, 4)$ and $R' = (7, 10)$, find $a$ and $b$.

Find the coordinates of the image of $P(1, 5)$ after a reflection in the line $y = x + 1$. (Hint: Midpoint and Perpendicularity)

If the radius of a circle is $5$ units, what is the circumference? (Leave in terms of $\pi$)

Which of the following is true for any circle?

What fraction of a circle is a sector with a $120^\circ$ central angle?

The region between a chord and the major arc is called the...

Two tangents are drawn to a circle from an external point $P$. If the tangents are $15$ cm long and the radius of the circle is $8$ cm, what is the distance from $P$ to the center?

The area of a sector with central angle $60^{\circ}$ is $6\pi$ cm$^{2}$. What is the circumference of the circle?

A chord $8$ cm long is at a distance of $3$ cm from the center of a circle. Find the diameter of the circle.

A circle has a chord $AB$ of length $10$ cm. The radius of the circle is $13$ cm. Point $C$ is on the major arc. What is the maximum possible area of triangle $ABC$?

The area of a segment of a circle is $25\pi - 50$ cm$^2$. If the radius of the circle is $10$ cm, what is the central angle of the segment?

A pendulum swings through an angle of $30^\circ$ and describes an arc $8.8$ cm in length. Find the length of the pendulum. (Use $\pi = \frac{22}{7}$)

A sphere's radius is $2$ cm. What is its volume in terms of $\pi$?

What is the volume of a rectangular prism with length $l$, width $w$, and height $h$?

A compound solid is formed by a cylinder of volume $50\pi$ and a cone of volume $20\pi$ on top. What is the total volume?

A cone has a radius of $3$ cm and a slant height of $5$ cm. What is its lateral surface area? (Formula: $LSA = \pi rl$). Leave in terms of $\pi$.

A soup can is a cylinder with a height of $12$ cm and a diameter of $7$ cm. What is the area of the label that covers the side of the can? (Use $\pi \approx \frac{22}{7}$)

What is the volume of a prism whose base is a triangle with base $10$ cm and height $4$ cm, and the prism height is $15$ cm?

A hemisphere has a volume of $18\pi \text{ cm}^3$. What is its radius?

If the volume of a cube is $x$ cm$^3$ and its surface area is $x$ cm$^2$, find the length of the edge of the cube.

A sphere has a surface area of $100\pi$ cm$^2$. If the radius is doubled, what is the new surface area?

A rectangular block of wood measures $10$ cm by $8$ cm by $6$ cm. A hole of diameter $4$ cm is drilled through the center of the $10$ cm $\times$ $8$ cm face all the way through to the other side. Calculate the volume of the remaining wood (use $\pi \approx 3.14$).

How many total faces are found in the net of a hexagonal prism?

In the net of a cone, the distance from the apex of the sector to any point on its arc is equal to what in the 3D cone?

If a net consists of 2 triangles and 3 rectangles, how many edges does the resulting 3D shape have?

How many total faces does the net of an octagonal pyramid have?

When folding a net into a 3D shape, a vertex is where at least how many faces meet?

A net of a rectangular prism has dimensions $2 \text{ cm}, 3 \text{ cm}, \text{ and } 4 \text{ cm}$. What is the area of the smallest rectangle in the net?

If the radius of the base of a cone is $r$ and the slant height is $l$, the area of the sector in its net is given by which formula?

The net of a cube is folded. If the distance between two specific corners on the net was $\sqrt{5}$ units (where each square has side $1$), what is the maximum possible 3D distance between these same two points after folding?

A net for a triangular prism has three rectangular faces with areas $30, 40,$ and $50$ $\text{cm}^2$. If the height of the prism is $10$ cm, find the total surface area of the prism.

A pyramid net has a square base with area $100$ $\text{cm}^2$. The total length of all edges in the 3D pyramid is $88$ cm. What is the perimeter of one of the triangular faces in the net?

In the formula $y = mx + c$, which letter represents the gradient?

Find the distance between points $(4, 4)$ and $(1, 0)$.

What is the gradient of the line passing through $(5, 2)$ and $(10, 7)$?

Determine the midpoint of $(-10, -2)$ and $(-2, -10)$.

Determine the distance between $(2, -2)$ and $(-1, 2)$.

Calculate the gradient of the line passing through $(3, 4)$ and $(1, 0)$.

Find the midpoint of $(12, 5)$ and $(0, 5)$.

The gradient of the line passing through $(2, -3)$ and $(b, 1)$ is undefined. What is the value of $b$?

Calculate the distance between the points $(a+b, a-b)$ and $(a-b, a+b)$.

If the line through $(4, 3)$ and $(1, y)$ is parallel to the line through $(0, 2)$ and $(-3, 0)$, find $y$.

If a line has a gradient of $-3$ and passes through $(0, 7)$, what is its equation?

A line has the equation $y = 0.5x + 2$. What is the y-coordinate when $x = 4$?

Find the gradient of the line passing through $(-1, -1)$ and $(1, 1)$.

What is the gradient of the line $y = 12$?

A line segment connects $(-3, 4)$ and $(3, 4)$. What is its length?

Find the gradient of the line $y = -x$.

Determine the midpoint of the segment with endpoints $(10, 20)$ and $(20, 30)$.

Find the point on the line $y = x + 2$ that is closest to the point $(4, 1)$.