📐 geometry

1. **State the problem:** We need to find the area of a shape composed of a rectangle ABDE and a right-angled triangle BCD attached along side BD. 2. **Given dimensions:**

1. **State the problem:** We have a trapezium with vertex $V$ and a center of enlargement located 2 units below and 1 unit left of $V$. The trapezium is enlarged by a scale factor

1. **Problem statement:** Given a circle with center O and points A, B, C, D, E on the circumference, where DE = DC, reflex angle EOC = 240°, and angle EAB = 100°. We need to find

1. **Problem statement:** Find (a)(ii) angle C B D, (a)(iii) angle B E A, (b) location of point O with reasons, (c) length of chord B C given radius 5 cm, and (d) explain why point

1. **State the problem:** We need to find the sum of the interior angles of a heptagon, which is a polygon with 7 sides. 2. **Formula:** The sum of the interior angles of any polyg

1. **Stating the problem:** Given a geometric figure with points A, B, C, D, E, and P, where angles at B and C are 60°, and segment BE = 3a, we are asked to find the length of BC.

1. **State the problem:** Find the area of each given shape. 2. **Formulas and rules:**

1. **State the problem:** We have a circle ACP with center O and a semicircle EAD with center P. The line BA is tangent to the circle ACP at point A. Given that \(\angle AOP = 113.

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