Question Type 6: Finding the area of a triangle Exercises

A triangle has two sides of lengths $12\text{ m}$ and $9\text{ m}$ with an included angle of $\dfrac{\pi}{6}$ radians. Find its area.

Two sides of a triangle measure $8.5\text{ cm}$ and $11.2\text{ cm}$ with an included angle of $47^\circ$. Find the area, correct to $1$ decimal place.

Find the area of a triangle with sides $14 \text{ cm}$ and $20 \text{ cm}$ and included angle $120^\circ$. Give an exact value and a decimal approximation.

A triangular sail has two edges of lengths $4.6 \text{ m}$ and $6.3 \text{ m}$ meeting at an angle of $75^\circ$. Find the area to the nearest $0.01 \text{ m}^2$.

Find the area of a triangle with sides $5\text{ cm}$ and $9\text{ cm}$ and included angle $\dfrac{\pi}{3}$. Give an exact value and a decimal approximation to 3 significant figures.

Triangle $ABC$ has sides $AB = 7\text{ cm}$ and $AC = 10\text{ cm}$ with included angle $\angle BAC = 30^\circ$. Find the area of $\triangle ABC$.

Find the area of a triangle with sides $18\text{ cm}$ and $25\text{ cm}$ and included angle $2.1$ radians. Give your answer to $3$ significant figures.

Two sides of a triangular field measure $3.2\text{ km}$ and $4.1\text{ km}$ with an included angle of $12^\circ$. Find its area to three decimal places.

Find the area of a triangle with sides $9\text{ cm}$ and $12\text{ cm}$ and included angle $135^\circ$. Express the exact value and a decimal approximation.

A triangular plot has two sides of lengths $32\text{ m}$ and $45\text{ m}$ that meet at an angle of $68^\circ$. Find the area of the plot to the nearest square metre.

A triangle has sides $23\text{ m}$ and $17\text{ m}$ with an included angle of $103^\circ$. Find its area, correct to the nearest square metre.

From a point $O$, two paths $OA$ and $OB$ of lengths $50\text{ m}$ and $65\text{ m}$ are laid out on bearings $020^\circ$ and $110^\circ$, respectively. Find the area of $\triangle AOB$.