# 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. Circle From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
2. Medians Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
3. Rhombus It is given a rhombus of side length a = 19 cm. Touch points of inscribed circle divided his sides into sections a1 = 5 cm and a2 = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
4. Rectangle In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
5. Rectangle vs square The rectangle has dimensions of 13 × 10, square 8 × 8. Which shape has more area and how much above?
6. Rhomboid Calculate the circumference and area of the rhomboid with sides 20 and 14, with their angle 50°.
7. Windows Calculate the area of masonry to build wall with dimensions of 9 m × 4 m with 4 windows of size 64 cm × 64 cm.
8. Carpet The room has rectangle shape with dimensions 4 m × 3.8 m. How many meters of carpet a width of 3 need to buy to cover the entire room?
9. Right Δ A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
10. Area of RT Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
11. Laws From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
12. Area 4gon Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°. Convert 270° to radians. Write result as multiple of number π.
14. Hypotenuse and height In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs. Determine the radius of the circle, if its perimeter and area is the same number.
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. Trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
18. Arc Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
19. Described Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
20. Intersections How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.

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