# Planimetrics - problems

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. Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
2. Diamond and diagonals
A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
3. Medians 2:1
Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b.
4. Decorative fence
The rectangular garden is 57 m long and 42 m wide. Calculate how much m² it will reduce if it encloses with a 60 cm wide decorative fence.
5. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
6. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
7. Lighthouse
Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
8. Find the 9
Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
9. Trapezium diagonals
It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
10. Isosceles triangle 8
If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
11. Cable car
Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
12. Area of rectangle
How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
13. Horizontal distance
The road has a gradient of 8%. How many meters will the road rise on a horizontal distance of 400m?
14. Cincinnati
A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
15. A screen
A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
16. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
17. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
18. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
19. Hands
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
20. Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?

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