# Planimetrics - math word 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. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
2. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
3. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
4. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
5. Area of RT Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
6. Circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
7. Reverse Pythagorean theorem Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
8. Widescreen monitor Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
9. It is rectangular? Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
10. Circle arc Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
11. Square diagonal Calculate length of the square diagonal if the perimeter is 476 cm.
12. Triangle Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and itsinterior angles.
13. Right Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
14. Two squares Two squares whose sides are in the ratio 5:2 have sum of its perimeters 73 cm. Calculate the sum of area this two squares.
15. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
16. Area of trapezoid The trapezoid bases are and 7 dm and 11 cm. His height is 4 cm. Calculate the area of trapezoid.
17. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
18. IS trapezoid Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
19. Steps How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
20. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.

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