📐 geometry

1. The problem involves finding the area and perimeter of an L-shaped polygon with given side lengths: 12 in (top), 19 in (right), 7 in (left), and 6 in (inner horizontal segment).

1. **Stating the problem:** We are given an L-shaped polygon with side lengths 18 cm (top), 4 cm (right outer vertical), 10 cm (left vertical), and 8 cm (bottom). There are interio

1. დავწეროთ ამოცანა: გვაქვს ორი დახრილი, რომლებიც სიბრტყესთან ქმნიან კუთხეებს $a$ და $b$, ხოლო ერთმანეთთან 60 გრადუსიან კუთხეს. წერტილი სიბრტყიდან დაშორებულია 26 სმ მანძილით. უნდა

1. **Problem Statement:** In the circle with center A, BD is a diameter, and $m\angle BAC = 85^\circ$. We need to find:

1. **Problem (a):** Two chords intersect inside a circle at point H. Given segments HK = 10.5, HJ = 28, and HN = 21, find HM. 2. **Formula:** When two chords intersect inside a cir

1. **State the problem:** We are given a circle with center Z and points Q, R, S, U, V on or inside the circle. We know QR = 4x - 2, SR = 10, ZU = 8, and ZV = 8. We need to find th

1. **Problem Statement:** Given a circle centered at $O$, with tangent segments $HK$ and $HI$ touching the circle at points $J$ and $I$ respectively. The segment $KI$ passes throug

1. **State the problem:** We have two intersecting lines forming an X at point P with angles labeled as follows: angle APK = $(8x-7)^\circ$, the angle on the right is $y^\circ$, an

1. **State the problem:** We have two intersecting lines forming an X shape with angles labeled as follows: the top angle is $(8x-7)^\circ$, the bottom angle is $(6x+3)^\circ$, and

1. **State the problem:** Reflect triangle ABC with vertices A(-5, 2), B(-6, -1), and C(-3, 0) over the line $x = -6$, then translate the image by the vector from $(0,0)$ to $(5,-1

1. **Problem Statement:** (i) Find the length of Site A along the lake shore.

1. **State the problem:** We are given a circle arc with points T and A on it, segment TA = 12, point N below T with segment TN = 5, and segment NA crossing the arc to A. We need t

1. **Problem statement:** Find the value of $x$ in each of the six circles based on the given angles. 2. **Important rules and formulas:**

1. The problem states we have a right triangle with two side lengths given: 12 cm and 39 cm, and we need to find the length of the third side $x$. 2. We use the Pythagorean theorem

1. **State the problem:** We are given a rectangular prism-like solid with a volume of 72.66 cubic inches and one dimension (height) of 2 inches. We need to find the area of the ba

1. **Stating the problem:** We are given cubes with edge lengths $e$ and need to complete the table for total surface area (T.A.) and volume (V).

1. **State the problem:** We have two parallel lines GI and JL cut by a transversal MH, creating several angles. We need to identify which pairs of angles are vertical angles. 2. *

1. **State the problem:** Find the volume of the given 3D prism-like figure with dimensions $a=16$, $b=9$, $c=21$, and other edges labeled 11 m and 24 m.

1. **State the problem:** Calculate the area of the given L-shaped compound shape with sides 4 cm, 2 cm, 3 cm, 1 cm, and 1 cm. 2. **Formula and approach:** To find the area of a co

1. **Stating the problem:** We are given various artworks with their dimensions and costs, and room sizes. The problem is to understand or analyze the geometry and dimensions of th

1. **Problem Statement:** Determine which sets of measurements could be the interior angle measures of a triangle and which sets could be the side lengths of a triangle. 2. **Trian