# 9th grade (14y) + Heron's formula - math problems

1. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
2. Described Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
3. Trapezoid Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm..
4. Triangle SSS Calculate perimeter and area of ​​a triangle ABC, if a=42, b=57 and c=42.
5. Prism Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
6. Cardboard box We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
7. Heron backlaw Calculate missing side in a triangle with sides 17 and 34 and area 275.
8. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
9. Circles 2 Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
10. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
11. Diamond Rhombus has side 17 cm and and one of diagonal 22 cm long. Calculate its area.
12. Sails We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
13. Triangle The triangle has known all three sides: a=5.5 m, b=5.3 m, c= 7.8 m. Calculate area of ​this triangle.
14. Triangle Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
15. The farmer The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
16. Sides ratio Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
17. Sss triangle Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
18. One trapezium One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.

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