📐 geometry

1. The problem involves a geometric figure with points A, B, C, D and given lengths: 14 cm, 7 cm, 10 cm, 1.75 cm, and 56 m, 30 m. 2. We are given conditions: i. \(\angle DÔC = \ang

1. **State the problem:** Calculate the perimeter of the given circular sectors with specified angles and radii. 2. **Formula for perimeter of a circular sector:**

1. **Problem statement:** We have a circle with center $O$ and two parallel chords $AB$ and $CD$.

1. **Stating the problem:** Find the perimeter of a sector (පරිමිතිය) given the angle and radius. 2. **Formula for the perimeter of a sector:**

1. **Problem Statement:** Given two equal circles with perimeter 360 m each, intersecting at points A, B, C, and D such that AC = DB and center O is the intersection of lines AD an

1. **Stating the problem:** We need to find the area of the quadrilateral formed under the line from (0,0) to (50,5) and including the shaded right triangle between points (20,0),

1. **State the problem:** We need to find the area of an irregular polygon composed of rectangles and a square with given side lengths in millimeters. 2. **Break down the figure in

1. **State the problem:** We need to find the surface area of a rectangular pyramid with base edges 20 cm and 36 cm, and heights 30 cm and 26 cm from the apex perpendicular to the

1. **State the problem:** We need to find the surface area of a triangular pyramid (tetrahedron) with a base that is an equilateral triangle of side length 15 inches, a height insi

1. **State the problem:** Find the area of triangle RST given angle $S = 37^\circ$, side $ST = 15$ cm, and side $RT = 12.5$ cm. 2. **Formula used:** The area of a triangle when two

1. **State the problem:** We know the area of a sector of a circle, $A$, varies directly as the angle of the sector, $\theta$, and the square of the radius, $r$. Given $r=6$ cm, $\

1. The problem is to find the area, but the specific shape or formula is not given. 2. To find the area, we need to know the shape (e.g., rectangle, triangle, circle) and the relev

1. **Problem statement:** We have triangle $ABC$ with centroid $G$. A line through $G$ intersects sides $AC$, $BC$, and $AB$ at points $P$, $Q$, and $R$ respectively. Given $AR > B

1. **State the problem:** We need to find the length of the flight of stairs, which is the hypotenuse of a right triangle with a height of 22 m and a base of 39 m. 2. **Formula use

1. مسئله: در مثلث $ABC$ که $AB=AC$ و زاویه $\hat{A}=80^\circ$ است، نقطه $D$ داخل مثلث قرار دارد به طوری که $\hat{D}\hat{B}C=10^\circ$ و $\hat{D}\hat{C}B=30^\circ$. باید ثابت کنیم م

1. مسئله: سه نقطه A، B و C روی یک دایره قرار دارند. دو ارتفاع AH و BG یکدیگر را در نقطه D قطع می‌کنند و امتداد AH با دایره در نقطه M برخورد می‌کند. باید ثابت کنیم پاره‌خط‌های DH و

1. **Problem Statement:** Find the values of variables $x$ and $y$ in Figure 17, where two intersecting lines form vertical angles labeled $(9x + 12)^\circ$, $3x^\circ$, and $(4y -

1. **State the problem:** We need to find the values of $x$ and $y$ in two figures using angle relationships such as supplementary angles, alternate exterior angles, and correspond

1. **Problem:** Find the coordinates of triangle DEF after each transformation. Given vertices: D(4, -1), E(5, 2), F(1, 2).

1. **State the problem:** We need to find the measure of angle $\angle B$ in a right triangle with vertices $B$, $C$, and $A$. The side $BC$ is perpendicular to $CA$, so $\angle C$

1. **State the problem:** We have an irregular polygon with given side lengths: 16 cm (top horizontal), 6 cm (right vertical), 11 cm (bottom horizontal segment), 4 cm (downward ver