IB Mathematics Analysis and Approaches 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 $\frac{\pi }{6}$ 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 $\frac{\pi }{3}$. 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 $△ABC$.

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 $△AOB$.