Geometry

Find the area of a rectangle with length $8$ cm and width $5$ cm.

Find the area of a triangle with base $10$ cm and height $6$ cm.

Find the area of a circle with radius $5$ cm. Give your answer in terms of $\pi$.

In a right-angled triangle, the legs are $3$ and $4$ cm. Find the hypotenuse.

A right-angled triangle has hypotenuse $10$ cm and one leg $6$ cm. Find the other leg.

Find the circumference of a circle with radius $4$ cm, in terms of $\pi$.

A ship sails due east. State its bearing.

Find the volume of a cuboid measuring $4$ cm × $5$ cm × $6$ cm.

In a right-angled triangle, the side opposite to angle $\theta$ has length $3$ cm and the hypotenuse is $5$ cm. Find $\sin\theta$.

Find the perimeter of a rectangle measuring $9$ cm by $4$ cm.

Find the area of a trapezium with parallel sides $6$ cm and $10$ cm, height $4$ cm.

A shape consists of a rectangle $8$ × $5$ with a right triangle (legs $4$ and $3$) attached. Find the total area.

A right-angled triangle has hypotenuse $10$ cm and angle $\theta = 30°$. Find the length of the side opposite $\theta$ (to 2 d.p.).

A right-angled triangle has hypotenuse $12$ cm and angle $\theta = 40°$. Find the side adjacent to $\theta$ (to 2 d.p.).

A right-angled triangle has adjacent side $8$ cm and angle $\theta = 35°$. Find the opposite side (to 2 d.p.).

In a right-angled triangle, the opposite side is $5$ cm and the hypotenuse is $10$ cm. Find $\theta$ (to 1 d.p.).

A walker travels on a bearing of $50°$, then turns right through $90°$. What is the new bearing?

Find the volume of a cylinder with radius $4$ cm and height $10$ cm, in terms of $\pi$.

A right-angled triangle has legs $2$ and $3$ cm. Find the hypotenuse exactly.

Find the area of a parallelogram with base $12$ cm and perpendicular height $7$ cm.

Find the area of a triangle with sides $a = 6$ cm, $b = 8$ cm, and included angle $C = 30°$ (to 2 d.p.).

A ship sails $50$ km on a bearing of $60°$. How far east and north does it travel? (1 d.p.)

A tree of height $12$ m casts a shadow of length $5$ m. Find the angle of elevation of the sun (to 1 d.p.).

In a triangle, $A = 50°$, $B = 60°$, and the side opposite $A$ is $8$ cm. Find the side opposite $B$ (to 2 d.p.).

In a triangle, two sides are $5$ cm and $7$ cm with included angle $60°$. Find the third side (to 2 d.p.).

A ship sails from A on a bearing of $60°$ to B, $10$ km away. From B, it sails on bearing $150°$ to C, $12$ km away. (a) State the angle $\angle ABC$. (b) Use cosine rule to find $AC$ (2 d.p.).

A right-angled triangle has hypotenuse $10$ cm and an angle of $30°$. Find its perimeter (to 2 d.p.).

Find the length of the space diagonal of a cuboid measuring $3$ × $4$ × $12$ cm (to 2 d.p.).

A pyramid has a square base of side $8$ cm and apex directly above the centre, $6$ cm above the base. Find the slant height from the apex to a midpoint of a base edge (to 2 d.p.).

A triangle has sides $5, 7, 9$ cm. Find the largest angle (to 1 d.p.).

A ship at $A$ sails on bearing $60°$ for $30$ km to $B$. From $B$ it sails on bearing $150°$ for $40$ km to $C$. Find the distance $AC$ (to 2 d.p.).

Find the area of a sector of a circle with radius $10$ cm and angle $60°$ (to 2 d.p.).

From a point $25$ m from the base of a tower the angle of elevation to the top is $38°$. Find the height of the tower (2 d.p.).

In triangle $ABC$, $a = 8$ cm, $b = 10$ cm, $A = 40°$. Find angle $B$ (to 1 d.p.).

A solid consists of a cylinder (radius $3$ cm, height $10$ cm) topped by a hemisphere (same radius). Find the volume in terms of $\pi$.

A triangle has sides $6, 8, 10$ cm. Use the cosine rule to find an angle, then compute the area (to 2 d.p.).

Two ships leave a port. Ship 1 sails on bearing $60°$ at $20$ km/h; Ship 2 on bearing $150°$ at $15$ km/h. How far apart are they after $2$ hours (to 2 d.p.)?

A ladder of length $5$ m leans against a vertical wall. The foot of the ladder is $3$ m from the wall. (a) How high up the wall does the ladder reach? (b) What angle does the ladder make with the ground (to 1 d.p.)?

In triangle $ABC$, $A = $50°$, $B = $70°$, and side $c = $10$ cm. Find side $a$ (to 2 d.p.).

A regular hexagon has side length $6$ cm. Find its area exactly (in surd form).