# 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. Ratio of perimeters Rectangle ABCD has dimensions 3 cm and 4 cm, KLMN rectangle has dimensions 4 cm and 12 cm. Calculate the ratio of the perimeter ABCD and perimeter KLMN.
2. Polygon 42 Which polygon has 42 more diagonals than sides?
3. Angles The outer angle of the triangle ABC at the vertex A is 114°12'. The outer angle at the vertex B is 139°18'. What size is the internal angle at the vertex C?
4. Trapezoid thirds The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
5. Saw Imagine that the saw blade with diameter 40 cm has one tooth colored with a different color. How long is path describing by the tip of the tooth after 15 minutes, if the blade is rotated 13365 times?
6. Perimeter of triangle In triangle ABC angle A is 60° angle B is 90° side size c is 15 cm. Calculate the triangle circumference.
7. Right triangle trigonometrics Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
8. ABS CN Calculate the absolute value of complex number -15-29i.
9. Rectangles - sides One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
10. Area of RT 2 Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm.
11. Equilateral triangle v2 Equilateral triangle has a perimeter 36 dm. What is its area?
12. 9-gon Sum of interiol angles of 9-gon is:
13. Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
14. Catheti The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
15. Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
16. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
17. Silver medal To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
18. Is right triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
19. Alfa, beta, gama In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
20. Wheel diameter A 1m diameter wheel rolled along a 100m long track. How many times did it turn?

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