📐 geometry

1. The problem is to draw the figure of a triangle. 2. A triangle is a polygon with three edges and three vertices.

1. **Problem Statement:** We have a rectangular field with perimeter 70 m. Its length is 15 m longer than its breadth. The field is surrounded by a concrete path with widths 5 m (t

1. **Problem Statement:** We are given a triangle with sides 7 cm, 13 cm, and 12 cm. We need to find the length of the perpendicular from the vertex opposite the side of length 12

1. **Problem Statement:** Calculate the angles $\angle C$ and $\angle A$ in triangle $\triangle ABC$ where $AB=AC$, $\angle B=25^\circ$, and $AG=3m$ with $AG=6D$ (interpreted as $G

1. ප්‍රශ්නය: ABC යනු ත්‍රිකෝණයක්. BAC හා ACB කෝණවලු සමමැද Luka F දක්වනත වෙ. AD සමකෝණ BC මත වන අතර G යනු CE හි මධ්‍ය ලක්ෂ්‍යයයි. BEGD කෘමිසයක් බව සාධනය කරන්න. 2. BEGD කෘමිසයක් බවට ස

1. Problem 11: Given triangle ABC with angles BÂC and AĈB equal, and F as the intersection of AD (median from A to BC) and CE (segment from C to E on AB), G is the midpoint of CE.

1. Problem 11 states that triangle ABC is right-angled, with angles BAC and ACB equal, and F is the midpoint of the hypotenuse BC. AD is perpendicular to BC, and G lies on CE such

1. **Problem 1: Find the value of $x$ given the equation $2x + 62 = 111$.\n\n2. Use the equation and isolate $x$: \n$$2x + 62 = 111$$\nSubtract 62 from both sides:\n$$2x = 111 - 62

1. Let's start with a basic geometry problem: Find the area of a triangle with base $b=10$ units and height $h=6$ units. 2. The formula for the area of a triangle is:

1. **Problem statement:** We need to find the size of angle $\theta$ in a cuboid where the edges meeting at $\theta$ are 3 mm and 14 mm, and the opposite edge is 8 mm. 2. **Underst

1. **Problem Statement:** A horse is tied to a peg at one corner of a square field with side length 15 m by a rope of length 5 m. We need to find the area of the part of the field

1. **Identify the statement that does NOT belong:** - The diagonals of a trapezoid are congruent. (False, trapezoid diagonals are generally not congruent)

1. Problem: If line M and N are both perpendicular to line S, then M and N are said to be ___. - When two lines are both perpendicular to the same line, they are parallel to each o

1. **Problem:** Prove that in a quadrilateral ABCD circumscribing a circle, the sum of the lengths of opposite sides are equal, i.e., $AB + CD = AD + BC$. 2. **Formula and rule:**

1. Problem 1: A circle is inscribed in a square of side 10 cm. Find the area of the circle in terms of $\pi$. - The diameter of the inscribed circle equals the side of the square,

1. **Problem Statement:** Find the area of the grassy border around a circular fountain with radius 5 m, where the grass border extends to 8 m from the center.

1. Let's state the problem: We have a rectangle with height 20, a trapezium with height 15 mm, and a parallelogram with height 15 mm. 2. To find areas of these shapes, we use the f

1. **Stating the problem:** We have a metal strip of length 150 mm and height 20 mm. From this strip, three congruent trapeziums and two congruent parallelograms are pressed out. W

1. Let's start by defining the shapes: a trapezoid is a quadrilateral with at least one pair of parallel sides, and a parallelogram is a quadrilateral with two pairs of parallel si

1. **Problem Statement:** Given that AD and BC are equal in length and both are perpendicular to the line segment AB, prove that the line segment CD bisects AB. 2. **Understanding

1. **Problem Statement:** Given that AD and BC are equal in length and both are perpendicular to the line segment AB, prove that the line segment CD bisects AB. 2. **Understanding