# 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. Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
2. Hexagon ABCDEF In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
3. Three sides Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
4. Spruce height How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
5. Lighthouse Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
6. Cutting square From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
7. Complementary angles 2 Two complementary angles are (x+4) and (2x - 7) find the value of x
8. Sss triangle Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
9. Diamond and diagonals A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
10. Area of rectangle How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
11. Perimeter of RT Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
12. Square metal sheet Four squares of 300 mm side were cut out from a square sheet metal plate with a side of 0,7 m. Express the fraction and the percentage of waste from the square metal sheet.
13. Infinite sum of areas Above the height of the equilateral triangle ABC is constructed an equilateral triangle A1, B1, C1, of the height of the equilateral triangle built A2, B2, C2, and so on. The procedure is repeated continuously. What is the total sum of the areas of all tri
14. Isosceles triangle The circumference of the isosceles triangle is 32.5 dm. Base length is 153 cm. How long is the leg of this triangle?
15. Isosceles trapezoid The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?
16. Land Rectangular triangular land has area 30 square meters and 12 meters long leg. How many meters of the fence do you need for fencing this land?
17. Square sides If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
18. Decorative fence The rectangular garden is 57 m long and 42 m wide. Calculate how much m² it will reduce if it encloses with a 60 cm wide decorative fence.
19. KLM triangle Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
20. Ruler and compass Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.

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