Calculate the area of the following triangles:
Calculate the area of the following triangles, to the nearest square centimetre:
Find the area of the following triangles, to one decimal place:
Sides lengths of 9.5 \text{ cm}, 10 \text{ cm} with an included angle of 47 \degree.
Sides lengths of 18.4 \text{ cm}, 20.5 \text{ cm} with an included angle of 99 \degree.
Find the exact area of an equilateral triangle with a side length of 6 \text{ cm}.
Find the exact area of an equilateral triangle with a perimeter of 24 \text{ cm}.
Consider the diagram of an isosceles triangle where h is the height perpendicular to base, b:
Form an expression for h in terms of \theta and a.
Find b in terms of \theta and a.
Form an expression for the area A of the larger triangle, in terms of \theta and a.
Consider the following parallelogram:
Find the area of the triangle formed by the points X, Y and Z, in terms of x, y, and \sin Z.
Hence, find the area of the parallelogram in terms of x, y, and \sin Z.
Use the sine rule to prove that the area of \triangle ABC is given by the equation: \text{Area} = \dfrac{a^{2} \sin B \sin C}{2 \sin A}.
The following triangle has an area of 520 \text{ cm}^{2}. Find the length of side b. Round your answer to the nearest centimetre.
The following triangle has an area of 150 \text{ cm}^{2}. Find the length of side b. Round your answer to the nearest centimetre.
The following triangle has an area of 200.52 \text{ cm}^{2}. Find the length of side b. Round your answer to two decimal places.
The following triangle has an area of 114.89 \text{ cm}^{2}. Find the length of side b. Round your answer to one decimal place.
\triangle ABC has an area of 99.3 \text{ cm}^{2}. The side AC = 14.5 \text{ cm} and \angle ACB = 25 \degree.
Find the length of CB. Round your answer to one decimal place.
Consider the diagram and find the angle x, correct to one decimal place:
Given the area and sides of a triangle, find the indicated angle correct to two decimal places:
In \triangle XYZ find \angle Y. Area = 75 \text{ cm}^2, XY = 13 \text{ cm}, YZ = 12 \text{ cm}.
In \triangle ABC find \angle B. Area = 19.84 \text{ cm}^2, AB = 7.36 \text{ cm}, BC = 5.45 \text{ cm}.
In \triangle LMN find \angle M. Area = 11.25 \text{ cm}^2, LM = 5.2 \text{ cm}, MN = 5.1 \text{ cm}, LN = 5 \text{ cm}.
In \triangle DEF find \angle D. Area = 44.9 \text{ cm}^2, DE = 10 \text{ cm}, DF = 13 \text{ cm}, EF = 9 \text{ cm}.
A triangular paddock has measurements as shown in the diagram:
Find the area of the paddock. Round your answer to the nearest square metre.
State the area in hectares. Round your answer to two decimal places.
An industrial site in the shape of a triangle is to take up the space between where three roads intersect.
Find the area of the site. Round your answer to two decimal places.
A triangular plot of land is being replaced by a park. The two sides of the park are 250\text{ m} and 350\text{ m} in length and the angle between them is 60 \degree. Find the area of the park to two decimal places.
The roads between Jaime, Jenna and Jill’s homes form a triangle. It is 2\text{ km} from Jaime to Jenna’s house and 3.5\text{ km} from Jaime to Jill’s house. The angle between these two roads is 85 \degree. Find the area enclosed by the roads between all three houses to two decimal places.
The Bermuda Triangle is an area in the Atlantic Ocean where many planes and ships have mysteriously disappeared. Its vertices are at Bermuda (B), Miami (M) and Puerto Rico (P):
Find the area of the Bermuda Triangle. Round your answer correct to two decimal places.
A student created a scale model of Australia and drew a triangle between Alice Springs, Brisbane and Adelaide:
Find the angle \theta, between Brisbane and Adelaide from Alice Springs. Round your answer to one decimal place.
Hence or otherwise, find the area taken up by the triangle. Round your answer to two decimal places.
For each rhombus below find the area:
The area of a rhombus is 17.37 \text{ cm}^2, while its acute angle is 44 \degree. Find its side length, a \text{ cm}.
The area of a rhombus is 44 \text{ cm}^2, while its side length is 8 \text{ cm}. Find the acute angle \theta of this rhombus.
Find the area of the parallelograms described below. Round your answers to two decimal places.
Adjacent side lengths of 12 \text{ cm} and 7 \text{ cm}, with an included angle of 101 \degree.
A hexagon has sides with length 10 \text{ cm}. Find the area of the hexagon leaving your answer in exact form.
An octagon is inscribed in a circle of radius 8 \text{ cm}.
Find the area of the octagon leaving your answer in exact form.
A regular pentagonal garden plot has centre of symmetry O and an area of 86 \text{ m}^2.
Find the distance OA.
The Australian 50 cent coin has the shape of a dodecagon (it has 12 sides). Eight of these 50 cent coins will fit exactly on an Australian \$10 note that is x \text{ cm} tall.
Find the total area of the eight coins in terms of x.
A regular n sided polygon is inscribed in a circle of radius r \text{ cm}.
Find the formula for the area of the n sided polygon, in terms of n and r.