Find the area of the following triangles:
Find the area of the triangle with base length 10 \text{ m} and perpendicular height 8 \text{ m}:
Consider the diagram of an isosceles triangle, where h is perpendicular to b:
Form an expression for h, the perpendicular height of the triangle in terms of \theta and a.
Find b, the base length of the triangle in terms of \theta and a.
Form an expression for the area of the larger triangle, in terms of \theta and a.
Calculate the area of the following triangles. Round your answers to two decimal places.
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.
Calculate the area of the following triangles, to the nearest square centimetre:
\triangle ABC has side a = 8\text{ cm}, side b = 5 \text{ cm} and \angle C = 40 \degree. Find the area of \triangle ABC to one decimal place.
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.
Find the area of a parallelogram with side lengths 4.6\text{ cm}, 6.8\text{ cm} and one internal angle of 42 \degree. 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.
Calculate the area of the site. Round your answer 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, Miami and Puerto Rico.
Find the area taken up by the Bermuda Triangle. Round your answer to the nearest square kilometre.
Find the area of the following triangles, to one decimal place:
9.5 \text{ cm}, 10 \text{ cm}, and included angle 47 \degree
18.4 \text{ cm}, 20.5 \text{ cm}, and included angle 99 \degree
Find the area of the following triangles, to one decimal place:
Find the area of the triangle with sides of length 5 \text{ cm}, 6 \text{ cm} and 5 \text{ cm}, using Heron's formula.
Find the area of the triangles with the following side lengths to one decimal place:
5 \text{ cm}, 5 \text{ cm} and 8 \text{ cm}
3.9 \text{ cm}, 1.7 \text{ cm} and 4.4 \text{ cm}
6 \text{ cm}, 5 \text{ cm} and 9 \text{ cm}
Find the area of the given quadrilateral:
Suppose an isosceles triangle has a perimeter of 50 \text{ cm} and its equals sides are of length 17 \text{ cm}.
Find the length of the third side.
Hence, find the area of the triangle.
Suppose a triangle has a perimeter of 44 \text{ cm} and two sides of length 11 \text{ cm} and 13 \text{ cm}.
Find the length of the third side.
Hence, find the area of the triangle.
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}.
Find the area of a parallelogram with adjacent sides of length 9 \text{ cm} and 10 \text{ cm}, and a diagonal of length 17 \text{ cm}.
Suppose a rhombus has a perimeter of 80 \text{ cm} and one of its diagonals is 24 \text{ cm}.
Find the length of each side of the rhombus.
Hence, find the area of the rhombus.
A triangle has sides of length 5 \text{ cm}, 12 \text{ cm} and 13 \text{ cm}.
Find the area of the triangle using Heron's Formula.
If the base length of the triangle is 13 \text{ cm}, find h, the perpendicular height of the triangle.
A triangular-shaped field has sides of length 25 \text{ m}, 29 \text{ m} and 36 \text{ m}.
Find the area of the field.
Kenneth has been hired to plough the field and to erect fencing around its perimeter. If he charges \$4 per square metre for ploughing and \$7 per metre for fencing, how much does he charge in total?
A triangle and a parallelogram have the same area and share a common base of 21 \text{ cm}. If the other sides of the triangle are 17 \text{ cm} and 10 \text{ cm}, find the height of the parallelogram.
A triangle has sides in the ratio 13:14:15 and a perimeter of 126 \text{ cm}.
Let the sides, in centimeters, be 13 x, 14 x and 15 x. Solve for x.
Hence, find the area of the triangle.
Consider a trapezium with parallel sides of length 19 \text{ cm} and 28 \text{ cm}, and non-parallel sides of length 10 \text{ cm} and 17 \text{ cm}.
Find the perpendicular height of the trapezium.
Hence, find the area of the trapezium.
\triangle ABC has an area of 520 \text{ cm}^{2}. The side BC = 48 \text{ cm} and \angle ACB = 35 \degree.
Find the value of b, to the nearest whole number.
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.
An isosceles triangle has an area 48 \text{ cm}^{2} and the length of its unequal side is 16 \text{ cm}. Let x be the length in \text{cm} of one of its equal sides.
Find an expression for the semi-perimeter of the triangle.
Hence, solve for x.
Find the area of the following rhombuses, correct to two decimal places:
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}. Round your answer to the nearest whole number.
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. Round your answer to the nearest degree.
A parallelogram has two adjacent sides of length 12 \text{ cm} and 7 \text{ cm} respectively, with an included angle that measures 101 \degree. Find the area of the parallelogram correct to two decimal places.
A hexagon has sides with length 10 \text{ cm}. Find the exact area of the hexagon.
An octagon is inscribed in a circle of radius 8 \text{ cm}. Find the exact area of the octagon.
A regular pentagonal garden plot has centre of symmetry O and an area of 86 \text{ m}^{2}. Find the distance OA, rounded to the nearest whole number.
The Australian 50 cent coin has the shape of a regular dodecagon (12 sided polygon). 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.
Calculate the fraction of the \$10 note that is not covered by coins.
A regular n sided polygon is inscribed in a circle of radius r \text{ cm}.
Determine the formula for the area of the n sided polygon, in terms of n and r.