# 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. Area of rectangle Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.
2. Isosceles Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
3. Quarter circle What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
4. Triangles Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?
5. Glass panel A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
6. ABCD square In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
7. Equilateral triangle A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
8. Largest angle of the triangle Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
9. Rectangular trapezoid The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the.
10. The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
11. Rectangular triangle The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
12. Equilateral triangle Calculate the area of an equilateral triangle with circumference 72cm.
13. Bamboo Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
14. Two rectangles I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
15. Coordinate axes Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
16. Diameter to area Find the area of a circle whose diameter is 26cm.
17. Enlarged rectangle The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
18. Diagonal to area Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
19. Painters Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
20. Triangles Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?

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