# 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. Isosceles trapezoid
Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
2. Regular n-gon
In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
3. Inner angles
The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
4. A map
A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
5. Photocopier
A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?
6. Type of triangle
How do I find the triangle type if the angle ratio is 2:3:7 ?
7. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
8. Trapezoid - RR
Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
9. Similarity coefficient
The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
10. Mirror
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
11. Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
12. Circle and rectangle
A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
13. Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
14. Square
Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
15. Thales
Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole.
16. Display case
Place a glass shelf at the height of 1m from the bottom of the display case in the cabinet. How long platter will we place at this height? The display case is a rectangular triangle with 2 m and 2.5 m legs.
17. Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
18. Rhombus EFGH
Construct the rhombus EFGH where e = 6.7cm, height to side h: vh = 5cm
19. Diameters of circles
How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm?
20. Diamond diagonals
Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.

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