# 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. Rectangle vs square The rectangle has dimensions of 13 × 10, square 8 × 8. Which shape has more area and how much above?
2. Trapezium zoom How many times increase area of trapezoid if all sides and altitude increase 5 times?
3. Rectangle - parallelogram It is given a rectangle that is circumscribed by a circle with a radius of 5 cm. The short side of the rectangle measures 6 cm. Calculate the perimeter of a parallelogram ABCD whose vertices are the midpoints of the sides of the rectangle.
4. Diamond Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
5. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
6. Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
7. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
8. Center traverse It is true that the middle traverse bisects the triangle?
9. Square If we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
10. Arc The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc?
11. Euclidean distance Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
12. Greatest angle Calculate the greatest triangle angle with sides 197, 208, 299.
13. ISO trapezoid v2 bases of Isosceles trapezoid measured 12 cm and 5 cm and its perimeter is 21 cm. What is the are of a trapezoid?
14. Base Compute base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm.
15. Construct 1 Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
16. Diagonal Diagonal of the rectangle has length 46.4 cm. Angle between diagonal and londer sife of rectangle is 22°. Calculate area of the rectangle.
17. Trapezoid IV In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
18. Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
19. TV diagonal Diagonal TV is 0.56 m long, how big the television sreen is if the aspect ratio is 16:9?
20. Plot The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan

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