📐 geometry

1. مسئله: مساحت مربعی را پیدا کنیم که یکی از رئوس آن نقطه $A(-1, 2)$ است و یکی از اضلاع آن روی خطی است که از نقاط $B(-1, 3)$ و $C(-4, -3)$ می‌گذرد. 2. ابتدا معادله خطی که از نقاط $

1. **Problem statement:** We have a right frustum ABCDSPQR with upper base rectangle PQRS (5 m by 2 m), lower base rectangle ABCD (15 m by 6 m), and height 12 m.

1. **Problem statement:** We need to find the area of a rhombus given the lengths of its diagonals, which are 9.2 cm and 7.5 cm. 2. **Formula:** The area $A$ of a rhombus can be ca

1. **Problem statement:** We need to find the value of $x$ in a right triangle where one leg is 2 units, the other leg is $x$ units, and the hypotenuse is 7 units. 2. **Formula use

1. **Problem Statement:** The Pythagorean theorem states that in a right triangle, the square of the hypotenuse length $c$ is equal to the sum of the squares of the other two sides

1. **Problem statement:** We have a cylindrical roller of diameter 25 units resting in a V-shaped groove with two sides inclined at 122° each. The horizontal distance between the g

1. **Problem Statement:** (i) Given AB = 7 cm and BC = 9 cm, prove that triangles ACD and DCB are similar, find length CD, and the ratio of their areas.

1. The problem asks us to classify a triangle with all three sides measuring 9 inches each. 2. The key formula or rule here is that a triangle with all three sides equal is called

1. The problem asks how to find the length of the third side of a right triangle when the lengths of the other two sides are known. 2. The key formula for right triangles is the Py

1. The problem asks whether describing a triangle as an acute triangle is a classification based on the lengths of its sides. 2. Let's clarify the types of triangle classifications

1. **Stating the problem:** We need to find the volume of a triangular pyramid (tetrahedron) with given edge lengths: base triangle sides 8 cm and 3 cm (height), and adjacent faces

1. **State the problem:** We need to find the volume of a trapezoidal prism with the following dimensions: top base $= 55$ m, bottom base $= 25$ m, height of trapezoid $= 20$ m, an

1. **State the problem:** We need to find the volume of a prism whose cross section is a parallelogram. The parallelogram has one pair of opposite sides 8 cm long and the distance

1. **Problem statement:** We need to find the volume of a prism whose cross section is a rhombus with an area of 24 cm² and length (height) of 10 cm. 2. **Formula used:** The volum

1. **Problem Statement:** Find the perimeter of the polygon formed by three hexagons arranged together, where one side length is given as 5.75 meters. The dotted lines represent in

1. **Problem Statement:** Find the perimeter of an equilateral triangle where each side measures 11 inches. 2. **Formula:** The perimeter $P$ of an equilateral triangle is given by

1. **State the problem:** We need to find the perimeter of an irregular polygon shaped like a U with given side lengths: left vertical segment = 6 yd, right vertical segment inside

1. **State the problem:** We need to find the perimeter of a hexagon with side lengths given as 5 inches, 5 inches, 9 inches, 9 inches, 5 inches, and 5 inches. 2. **Recall the form

1. **State the problem:** We need to find the perimeter of a square where each side measures 16 inches. 2. **Formula for perimeter of a square:** The perimeter $P$ of a square is g

1. The problem asks us to identify the polygon shown as an arrow pointing upward and find the sum of the measures of its interior angles. 2. To identify the polygon, count the numb

1. **Problem Statement:** Decide whether the statement "The perimeter of a pentagon is five times the length of one side" is true or false. 2. **Formula for Perimeter of a Polygon: