# 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. Triangle Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
2. SAS triangle The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
3. Rhombus Find the length of each side of rhombus if the perimeter is 49 dm long.
4. Similarity Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
5. Square If we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
6. Rhombus Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm.
7. Square Number If to a square of integer number add 17, we get the square of next integer number. What is the original number?
8. 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
9. Segment Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
10. Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
11. 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?
12. QuizQ An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
13. Height Calculate height of the equilateral triangle if its perimeter is 8?
14. Squaring the Circle Calculating side of the square with the same area as the circle of radius 18.
15. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
16. Clock How many times a day hands on a clock overlap?
17. Climb On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went? Calculate how many g's (gravity accelerations) feel glider pilot when turning the horizontal circles of radius 148 m flying at 95 km/h. Centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius of rotatio
19. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
20. OK circle Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17.

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