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
- Trapezoid
Calculate the area of trapezoid ABCD with sides |AB|= 78 cm, |BC|=51 cm, |CD|=15 cm, |AD|=30 cm.. - Circles 2
Calculate the area bounded by the circumscribed and inscribed circle in a triangle with sides 29 cm, 16 cm, and 21 cm. - 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. - 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? - Annulus from triangle
Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm. - 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? - Triangle area
A triangle with a circumference of 69 cm has one side three times shorter than the longest of them and the other 3 cm shorter than the longest of them. Find the area of the triangle. - 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 - Triangle land fencing
The land has the shape of an obtuse triangle with sides of 40m, 30, and 60m. Determine the minimum mesh length for fencing and the land area in ares. - 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 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. - 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. - Triangle
In triangle ABC, there is a point S with the center of the inscribed circle. The area of quadrilateral ABCS is equal to four-fifths of the area of triangle ABC. The lengths of the sides of triangle ABC expressed in centimeters are all integers and the - 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 - 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? - 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. - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and areas if given a=40cm, b=57cm, and c=59cm. - Parallelogram perimeter area
The parallelogram has side a = 58cm and diagonals u = 89cm and v = 52cm. Calculate the perimeter and area of this parallelogram. - Heron backlaw
Calculate the unknown side in a triangle with sides 39 and 38 and area 438.6.
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