# 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.- 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Map scale

On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters? - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Angles ratio

The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss) - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - V-belt

Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm - Tree shadow

The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Trapezoid MO-5-Z8

Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm^{2}. What is the area of the trapezoid KLMN? - Circular segment

Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ) - Trapezoid 15

Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4 - Isosceles right triangle

Contents of an isosceles right triangle is 18 dm^{2}. Calculate the length of its base. - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Rectangle

Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width. - Diagonals

Draw a square ABCD whose diagonals have a length of 6 cm - Equilateral triangle

The equilateral triangle has a 23 cm long side. Calculate its content area. - Double ladder

The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? - Rhombus

If we increase the rhombus side by 2.4 cm; its perimeter is 20 cm. How long was the side of the rhombus? - Square

Calculate the perimeter and the area of square with a diagonal length 30 cm. - Isosceles triangle

Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.

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