# Planimetrics - problems - page 46

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
2. Equation of circle 2
Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
3. Bathroom 2
A bathroom is 2.4 meters long and 1.8 meters wide. How many square tiles 1 dm on each side are to be used to cover it?
4. Rainfall
How many liters of water did fell in a 32m long and 8m wide garden, if 8mm of rain fell?
5. Fence and scale
The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made?
6. Photocopier
A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
7. Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
8. Lighthouse
The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow shorter by 3 meters. How tall is the lightho
9. Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
10. Trapezium bases
Find the trapezium height if a = 8 cm and c = 4 cm if its content 21 square centimeters.
11. Trapezoid ABCD
ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD.
12. A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
13. Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
14. Square area
Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area .
The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
16. Two forces
The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
17. Windbreak
A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
18. Clouds
Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
19. Diamond
The diamond has a circumference of 48cm. Calculate the length of its side in dm.
20. A square
A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.

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