📐 geometry

1. **Problem Statement:** We have a rectangular prism with surface area 80 square units. The prism shown is 5 units long, 4 units wide, and 2 units high. We want to find other rect

1. **Stating the problem:** We have a cone with height 120 cm and base diameter 80 cm (thus radius 40 cm). Inside it, a cylinder is inscribed with height $h$ and radius $r$. We wan

1. The problem states that we have a point $A$ with coordinates $(3,1,2)$ in 3D space. 2. This is a straightforward identification of a point in three-dimensional Cartesian coordin

1. დავიწყოთ ამოცანის დასმით: იპოვოთ კუთხე \(\angle ABC\), თუ \(\angle ABC = 260^\circ\).\n\n2. აქ მოცემულია, რომ \(\angle ABC\) უკვე არის 260 გრადუსი, რაც არ არის ჩვეულებრივი კუთხი

1. The problem asks to find the distance between the centers of two circles with radii 5 cm and 8 cm, respectively. 2. When two circles are tangent externally, the distance between

1. The problem is to understand the properties and calculations related to triangles. 2. A triangle is a polygon with three edges and three vertices.

1. The problem is to understand what polygons are and their basic properties. 2. A polygon is a closed plane figure with at least three straight sides and angles.

1. **Stating the problem:** We are given a circle with center $O$, chords $AB$ and $AC$ equal in length, and point $E$ on the extension of $AO$ intersecting chord $DC$. We need to

1. The problem states that $DF = DE + EF = 11 + 4 = 15$ meters, but the length is given as 11.7 meters without using the hypotenuse formula. 2. This suggests that $DF$ is the sum o

1. **State the problem:** We have a polygon ABCDEF with given conditions: BCD is a straight line, CA is parallel to DF, angles ABD, BDE, and DEF are right angles, and lengths AB =

1. **State the problem:** We need to find the translation that maps Figure T onto Figure U. 2. **Identify coordinates:**

1. **State the problem:** We have a prism with two regular hexagonal faces, each with an area of 23 cm². The height (length) of the prism is 8 cm, and the edge length of the hexago

1. **Problem Statement:** We have a prism with a regular decagonal cross-section. Each side of the decagon is 2 cm, and the height of the prism is 14 cm.

1. **State the problem:** We need to find the surface area of a triangular prism with given dimensions. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 7 m, 4 m, and 3 m, and the prism length (height) is 11 m. 2. **

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 7 m, 9 m, and a height of 3 m to the base 7 m, and the prism le

1. **State the problem:** We need to find the surface area of a triangular prism with a right triangle base where the legs are 7 m and 4 m, the hypotenuse is 9 m, and the prism hei

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base of base $8$ cm and height $15$ cm, a slant edge of $17$ cm, and prism length

1. **Problem Statement:** We have a right prism with an equilateral triangle base of side length 7 cm and a prism height (length) of 8 cm.

1. **Problem statement:** We have a prism with an equilateral triangular cross-section. The base of the triangle is 7 cm, and the prism's length (depth) is 8 cm.

1. **Problem statement:** We have a triangular prism with an equilateral triangle cross-section where each side of the triangle is 7 cm, and the length of the prism is 8 cm.