# 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. Black diamond run Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet.
2. An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
3. The angle of view Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.
4. The playground The playground has the shape of a square with a side of 64 m. It is fenced on three sides. What is the area of the playground and how long is its fence?
5. Two groves Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
6. Medians in RT The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
7. Horses playground The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
8. Outside tangents Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside.
9. Compute 4 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
10. Decide 2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
11. Chord BC A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
12. Right angle If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
13. Squares ratio The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
14. Five-gon Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
15. Annulus Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
16. Coordinates of a centroind Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
17. Two gardens The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
18. Power line pole From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
19. Free space in the garden The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large
20. Steps Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...