# 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.- 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. - 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. - 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. - A map

A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions? - 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? - Type of triangle

How do I find the triangle type if the angle ratio is 2:3:7 ? - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - 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 - 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 ". - 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. - Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. - 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. - 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? - 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? - 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. - 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. - 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? - Rhombus EFGH

Construct the rhombus EFGH where e = 6.7cm, height to side h: vh = 5cm - 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? - Diamond diagonals

Calculate the diamond's diagonal lengths if its content is 156 cm^{2}and the side length is 13 cm.

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