Planimetrics - math word problems - page 40 of 169
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.Number of problems found: 3378
- Rectangles - sides
One side of the rectangle is 10 cm longer than a second. Shortening the longer side by 6 cm and extending the shorter by 14 cm increases the rectangle area by 130 cm². What are the dimensions of the original rectangle? - Constructed 8161
The perimeter of the right triangle is 18 cm. The sum of the areas of the squares constructed above its three sides is 128cm². What is the area of the triangle? - Quadrilateral 7583
For the sizes of the interior angles of the quadrilateral ABCD, the following applies: the angle alpha is 26° greater than the angle beta, twice the angle Beta is 5° less than the angle gamma, and the angle gamma is 36° greater than the angle delta. Deter - Circumference 6312
The triangle has a circumference of 35 cm. The first side is four centimeters larger than the second and, at the same time, 1 cm larger than the third side. Determine the sides of the triangle. - Difference 3994
In a trapezoid, the difference is a base of 6 cm. Calculate the lengths of the bottom of a trapezoid when its height is 8 cm and the area of the trapezoid is 168 cm square. - Dimensions 3159
The rectangle is 6 cm longer than the width. A square with a side equal to the length of the rectangle has an area of 78 cm² larger than the rectangle. Calculate the dimensions of the rectangle. - Michael 2
Michael has a 35-foot ladder leaning against the side of his house. If the bottom of the ladder is 21 feet away from his house, how many feet above the ground does the ladder touch the house? - Quadrilateral
The perimeter of a quadrilateral (four-sided plane shape) is 125 cm. How long is the fourth side of the three known sides measure a=12 cm, b=45 cm, and c=30.5 cm? - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Concentric circles
There is given a Circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area? - Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - A truck
A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)? - In a 2
In a thirteen-sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal, and the other four are 18° less than each of the equal angles. Find the angles. - Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm. - Trapezoid
How long are the trapezoid bases with an area of 24 cm² and a height of 3 cm? One base is three times longer than the shorter. - The rope
A 68-centimeter-long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimeters. What is the distance between the other two corners? - Approximate 83298
They planted 5,600 tulips in the garden bed, an average of 50 tulips per 1 m². What is the approximate size of the flower bed? - Perimeter 31761
Mr. Marek wants to build a circular pond in his garden. He wishes the perimeter of the pond in meters and the area in square meters to be expressed in the same numbers. What is the radius of the pond? - Six-fourteenths 7295
Seven twelfth windows in the castle are in the shape of an n-gon. Six-fourteenths of these windows are quadrangular in shape, while two-ninths of them are square windows. How many windows are there in the castle if there are 15 square windows? - Circumference 7065
In an isosceles triangle, the length of the base is equal to 75% of the arm's length. Determine the area of the triangle if the circumference is 22 cm.
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