# 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. 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?
2. Ditch Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.
3. Area of iso-trap Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
4. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
5. Diagonals What x-gon has 54 diagonals?
6. Right triangle eq2 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
7. Rectangles The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
8. Find the 3 Find the distance and mid-point between A(1,2) and B(5,5).
9. Same area There is a given triangle. Construct a square of the same area.
10. The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle. 5 triangles + 1 square = how many sides in all
12. A rectangle A rectangle has an area of 36 cm2. What could the length and width of rectangle be?
13. Scale of plan On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares.
14. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increa The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
16. 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?
17. Area of a triangle What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3?
18. Two gardeners The garden with an area of 81 square meters was divided by two gardeners in a ratio of 4: 5. How much did the second gardener get more first?
19. Rhombus The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
20. Ratio of sides 2 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.

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