📐 geometry

1. **State the problem:** We have a parallelogram RSTU with diagonals intersecting at point M. Given lengths are $RS=9$, $ST=20$, and $RM=11$. We need to determine which segment is

1. **Problem statement:** Calculate the volume of wood used for two wooden tubs (trækær 1 and trækær 2) and their capacities in liters.

1. The problem is to match each highlighted sector in the pie charts to its correct angle measure. 2. Recall that a full circle is 360° and sectors are portions of this circle.

1. **State the problem:** We need to find the area of an L-shaped polygon composed of three segments: a top horizontal segment of length 1, a right vertical segment of length $x$,

1. **Problem statement:** We are given a quadrilateral with interior angles labeled $x$, $y$, $z$, and $w$. We need to find the value of $x + y + z + w$. 2. **Formula and rule:** T

1. The problem states that the distance around the edge of a circular swimming pool is 29 m. This distance is the circumference of the circle. 2. The formula for the circumference

1. The problem states: The circumference of a circle is 21 cm. We need to find the diameter of the circle, rounded to 1 decimal place. 2. Recall the formula for the circumference o

1. **Problem statement:** Calculate the size of angle $BCD$ given that angle $ABC$ is $128^\circ$ and the triangle has vertices $A$, $B$, $C$, and $D$ with $AB$ vertical and $AD$ h

1. **Problem statement:** We have a right triangle WZX with a right angle at X, angles \(\theta = 73^\circ\) at Y and \(\beta = 37^\circ\) at Z, and base \(ZY = 349\) units. We nee

1. **State the problem:** We need to find the missing side length $x$ (side AB) in triangle ABC, where side AC = 3.2, angle B = 44.1°, and angle C = 58°. 2. **Find the missing angl

1. The problem is to find the formula for the surface area (SA) of a triangular prism. 2. A triangular prism has two triangular bases and three rectangular faces connecting the cor

1. **Problem statement:** Find the surface area of the parallelogram prism with base sides 7 mm and 5 mm, height 4 mm, and an additional right triangle height 3 mm. 2. **Formula fo

1. **Stating the problem:** We have a polygon with a rectangular base of 15 cm, two vertical sides of height $h$, and a top side divided into three segments: two angled segments of

1. **Problem Statement:** Calculate the perimeter and height $h$ of the bottom-center polygon, which consists of a trapezoid with a base of 15 cm, two right triangles on top with s

1. **Problem statement:** An isosceles triangle has two sides of length 11 cm each, and its area is 40 cm². We need to find the sizes of the interior angles to the nearest degree.

1. **State the problem:** We have a circle with center O and an inscribed triangle ABC. The central angle \(\angle AOB = 160^\circ\) and we need to find the inscribed angle \(x = \

1. **Problem statement:** Calculate the total area of a window shaped as a rectangle with length 9 ft and height 6 ft, capped on each short side by a semicircle with radius 3 ft. 2

1. **State the problem:** We need to find the value of $e$ given that two lines intersect perpendicularly, forming four angles: one angle is $115^\circ$, another is $(5e)^\circ$, a

1. **State the problem:** We have a triangle with vertices T, V, and U. Given:

1. **State the problem:** We need to find side $g$ (EF) in triangle EGF where angle $G = 101^\circ$, side $EG = 5$, and side $GF = 4$. 2. **Formula used:** The Law of Cosines state

1. The problem asks to identify the quadrilateral based on the given side lengths and properties. 2. The quadrilateral has two pairs of opposite sides marked as equal: one pair wit