📐 geometry

1. **Stating the problem:** Máme štvouholník ABCD s podmienkami:

1. **Problem Statement:** We have a parallelogram GRPC with points B and E such that triangle GCB and triangle BPE are formed. Given lengths: $GC=375$ ft, $CB=325$ ft, $GB=425$ ft,

1. **State the problem:** We have a rectangle ABCD with AB = 8 and BC = 6. We need to find the lengths of AD, DC, and AC. 2. **Recall properties of a rectangle:** Opposite sides ar

1. **State the problem:** We are given a parallelogram ABCD with side AB = 5 units, side BC = 3 units, and angle at vertex B = 60°. 2. **Recall properties of parallelograms:** Oppo

1. **State the problem:** We need to find the area of a polygon shaped like the number "9" on a grid where each square is 1 cm by 1 cm. The polygon has a square hole inside it, so

1. **State the problem:** We need to find how many 4 feet by 9 feet panels are required to cover the outside perimeter of the structure. 2. **Identify the total perimeter length:**

1. **Stating the problem:** We have a ladder 3.5 m long leaning against a wall.

1. **State the problem:** We need to find the area of the shaded shape WXZY, which is the ring-shaped region between two sectors OWX and OYZ. 2. **Given data:**

1. **Problem Statement:** We are given a triangle with angles $E=30^\circ$, $F=57^\circ$, and $B=27^\circ$. We need to find the measure of angle $A$. 2. **Recall the Triangle Angle

1. **Problem statement:** We are given a large right triangle with vertices A, B, and I, and inside it smaller angles C = 83°, F = 105°, and E = 37°. We need to find the measure of

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 38 cm and 18 cm, and legs of 16 cm (height) and 20 cm. 2. **Formula for the area of a trapez

1. **State the problem:** We need to find the area of a parallelogram with a base of 8 cm and a height of 5 cm. 2. **Formula for the area of a parallelogram:**

1. The problem asks why the gradient of the perpendicular bisector of segment AB is -2. 2. First, recall that the gradient (slope) of a line perpendicular to another line is the ne

1. The problem asks to find the value of $x$ in the triangle where the angles are $86^\circ$, $2x$, and $4x$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angl

1. **Stating the problem:** We are given a set of angles with relationships involving $x$, $2x$, $y$, and known angles $132^\circ$ and $47^\circ$ in a figure with parallel lines. 2

1. **Problem 1:** In the circle ABCDE, CE is a diameter. Given \(\angle BAC = 36^\circ\), find \(\angle BDE\). 2. **Key fact:** The angle subtended by a diameter in a circle is a r

1. **Stating the problem:** We have a triangle with vertices J (top), M (bottom), and K (right). Given that $JK = MK$, we need to find the length of $JM$. 2. **Understanding the pr

1. **Problem statement:** Given a circle with center O and points A, B, C on the circumference, we know \(\angle ABO = 32^\circ\) and \(\angle BOC = 160^\circ\). We need to find \(

1. **State the problem:** We have a right triangle where one leg is 4 m less than the hypotenuse, and the other leg is 2 m less than the hypotenuse. We need to find the length of t

1. **State the problem:** We need to find the volume of a right-angled triangular prism with base sides 23 m and 38 m, and depth 11 m. 2. **Formula for volume of a prism:**

1. **Problem statement:** Calculate the perimeter (omkretsen) of the figure composed of straight lines and quarter circle arcs. Each square side length is 0.5 cm. Round the answer