Geometry and Measure

Calculate the area of the triangle shown in the diagram.

What is the order of rotational symmetry for the equilateral triangle shown?

Which mathematical name best describes the 3D shape shown in the diagram?

Calculate the area of the square shown in the diagram.

Calculate the area of the parallelogram shown in the diagram.

A coordinate grid shows point $A$ at $(2, 3)$. If point $A$ is reflected in the x-axis, what are the new coordinates?

Find the value of $z$ using the properties of angles on a straight line.

A coordinate plane shows a triangle with vertices at $P(2, 2)$, $Q(6, 2)$, and $R(4, 7)$. If the triangle is translated $3$ units to the left and $1$ unit up, what are the new coordinates of vertex $R$?

A piece of paper is in the shape of a kite. The diagonals are $16$ cm and $30$ cm long. What is the area of the kite?

A surveyor needs to find the height of a vertical pole $AB$. He stands at point $C$ and finds that $\triangle ABC$ is a right-angled triangle with the right angle at $B$. If the angle of elevation $ACB$ is $45^\circ$ and the distance $BC$ is $15$ m, what is the height of the pole?

A rhombus has an angle of $55^{\circ}$. What is the size of the opposite angle?

In the diagram, a straight line is drawn through a vertex of a triangle. Find $z$.

Identify the value of $x$ in this equilateral triangle.

Find the value of $k$ in the following kite.

Find the value of $x$ in the following arrow-head quadrilateral (concave).

In the diagram, $L1$ and $L2$ are parallel. Find the angle $c$.

A quadrilateral has angles $x$, $x+20$, $x+40$, and $x+60$. Find the value of $x$.

In a rectangle $ABCD$, point $E$ lies on $CD$ such that triangle $ADE$ is isosceles with $AD = DE$. If $AD = 5$ cm and the length of the rectangle $AB$ is $12$ cm, find the measure of $\angle EBC$ to the nearest degree.

A decorative tile is shaped like a concave quadrilateral $ABCD$ (an arrowhead or dart). If the reflex angle at $D$ is $240^{\circ}$, and the interior angles at $A$ and $C$ are $35^{\circ}$ each, find the interior angle at $B$.

In triangle $LMN$, the side $LN$ is extended to $P$. If the exterior angle $\angle MNP = 135^{\circ}$ and the interior angle $\angle L = 2x - 10^{\circ}$ and $\angle M = 3x + 20^{\circ}$, find the value of $x$.

Reflect the point $L(-3, 2)$ in the $y$-axis. What are the coordinates of the image $L'$?

A point $K(2, 5)$ is translated to $K'(6, 5)$. What is the translation vector?

Which of these lines is the line of reflection for the two shapes shown?

A shape is rotated $180^\circ$ about the origin. If a point on the shape is at $(4, -1)$, what are the coordinates of the image point?

Point $Z(4, 1)$ is rotated $90^\circ$ clockwise about the point $(2, 1)$. What are the coordinates of $Z'$?

A shape is translated such that $(x, y) \to (x-2, y+4)$. If the image of a point is $(0, 0)$, what was the original point?

Triangle $LMN$ is reflected in the line $y = -x$. If $L$ is at $(1, 2)$, what are the coordinates of $L'$?

A rectangle $ABCD$ has coordinates $A(-4, -1)$, $B(-2, -1)$, $C(-2, -4)$, and $D(-4, -4)$. The rectangle is translated by $\begin{pmatrix} 6 \\ 0 \end{pmatrix}$ and then reflected across the line $x = 1$. Where is the image of point $B$ located?

An L-shaped bracket is defined by points $L_1(1, 1)$, $L_2(1, 3)$, $L_3(2, 3)$, $L_4(2, 2)$, $L_5(3, 2)$, and $L_6(3, 1)$. The bracket is rotated $180^{\circ}$ about the point $(2, 2)$. What is the image of the point $L_2(1, 3)$?

A map shows a small forest as a triangle with coordinates $F_1(1, 2)$, $F_2(1, 4)$, and $F_3(4, 2)$. To create a mirrored park, the forest is reflected across the $y$-axis and then rotated $90^{\circ}$ counter-clockwise about the origin. What is the final coordinate of the image of $F_3$?

A cube has a surface area of $24\text{ cm}^2$. What is the area of one face?

Find the perimeter of an equilateral triangle with a side length of $11\text{ cm}$.

Calculate the area of a parallelogram with base $9\text{ cm}$ and height $4\text{ cm}$.

The diagram shows a circle with radius $7\text{ cm}$. Using $\pi \approx \frac{22}{7}$, calculate its circumference.

A garden path is designed using a large rectangle and a smaller rectangular cutout for a flower bed. The dimensions of the large rectangle are $12\text{ m}$ by $8\text{ m}$. The flower bed is a rectangle measuring $5\text{ m}$ by $3\text{ m}$. Calculate the area of the shaded path.

The perimeter of a rectangle is $28\text{ cm}$. If the length is $9\text{ cm}$, find the area.

A triangle has an area of $60\text{ cm}^2$ and a base of $15\text{ cm}$. What is its height?

A rectangular sheet of metal measures $20\text{ cm}$ by $15\text{ cm}$. A square of side $x\text{ cm}$ is cut from each corner to make an open box. If $x = 3\text{ cm}$, what is the volume of the box?

A storage container is made of two parts: a cuboid base and a triangular prism top. The base is $5\text{ m}$ long, $3\text{ m}$ wide, and $2\text{ m}$ high. The triangular prism has the same length and width, with a height of $1.5\text{ m}$. Calculate the total volume.

A circular garden has a diameter of $14\text{ m}$. A circular fountain of radius $2\text{ m}$ is built in the center. What is the area of the garden remaining for grass? (Use $\pi \approx \frac{22}{7}$)

A box weighs $0.05$ tonnes. How many kilograms ($kg$) is this?

A car travels $12$ kilometers ($km$). How many meters ($m$) did it travel?

A bottle contains $500$ ml of juice. If you have $4$ such bottles, how many liters ($L$) of juice do you have in total?

The height of a door is $210$ cm. What is its height in meters ($m$)?

A rectangle has a length of $0.45\text{ m}$ and a width of $28\text{ cm}$, as shown in the diagram. Calculate the area of the rectangle in square centimetres ($\text{cm}^2$).

A map has a scale of $1 : 50,000$. A road on the map is $4 cm$ long. What is the actual length of the road in kilometers ($km$)?

A rectangular swimming pool is $25 m$ long and $10 m$ wide. If it is filled to a depth of $2 m$, what is the volume of water in cubic centimeters ($cm^3$)?

A construction company is building a rectangular foundation for a storage unit. The blueprint shows the foundation has a length of $4.5$ m and a width of $350$ cm. To ensure stability, the foundation must be filled with concrete to a depth of $200$ mm. Calculate the total volume of concrete required in cubic metres ($m^3$).

A cube has a surface area of $150$ $cm^2$. What is the volume of the cube in cubic millimeters ($mm^3$)?

The diagram shows a composite shape made of two rectangles. Find the total area of the shape in square millimeters ($mm^2$).