Heron's formula - practice problems - page 2 of 4
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 72
- Circles 2
Calculate the area of the region between the circumscribed circle and the inscribed circle of a triangle with sides 29 cm, 16 cm, and 21 cm. - The perimeter
The perimeter of a rhombus whose diagonal lengths are in the ratio 3:4 is 40 cm. What is its area in cm²? - Sides of the triangle
Calculate triangle sides where its area is S = 84 cm² and a = x, b = x + 1, xc = x + 2 - Circle inscribed
There is a triangle ABC and a circle inscribed in this triangle with a radius of 15. Point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26? - Annulus from triangle
Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25 mm, b = 29 mm, c = 36 mm. - Triangle sides to angles
The triangle ABC has side lengths a = 14 cm, b = 20 cm, c = 7.5 cm. Find the sizes of the angles and the area of this triangle. - Triangle angle area
Calculate the size of the largest angle in triangle ABC if a = 7 cm, b = 8 cm, and c = 13 cm. Calculate the area of the triangle, the height per side a. - Measurements of a triangle
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. A = 50°, b = 30 ft, c = 14 ft - General triangle
Given a general triangle ABC. Its perimeter is 30 cm, with side a=2 cm longer than side b and 5 cm shorter than side c. Determine the area of the triangle. - Triangle land fencing
The land has the shape of an obtuse triangle with sides of 40 m, 30, and 60 m. Determine the minimum mesh length for fencing and the land area in ares. - Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8 cm, b = 11 cm, c = 12 cm - Triangle height calculation
The sides of the ABC triangle measure 39 cm, 42 cm, and 45 cm. The second-longest height of this triangle is 36 cm. What is its shortest height? - Triangle
In triangle ABC, point S is the incentre (centre of the inscribed circle). The area of quadrilateral ABCS equals four-fifths of the area of triangle ABC. The side lengths of triangle ABC are all integers expressed in centimetres, and the perimeter of tria - Triangle solving calculation
Solve the triangle ABC if the side a = 52 cm, the height on the other side is vb = 21 cm, and the triangle's area is S = 330 cm². - Triangle
Determine whether we can make a triangle with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 119 b = 170 c = 130 - Circumscribed circle
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Circumscribed circle ABC
Triangle ABC, with sides a = 15 cm, b = 17.4 cm, and c = 21.6 cm, is circumscribed by a circle. Calculate the area of the segments determined by the sides of the triangle. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and areas if given a=40 cm, b=57 cm, and c=59 cm. - Compute 4
Compute the exact value of the triangle area with sides 14 mi, 12 mi, and 12 mi long.
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