📐 geometry

1. **Problem:** Find the area of a trapezoid with parallel sides 13 cm and 21 cm, the longer non-parallel side 17 cm, and the shorter side perpendicular to the parallel sides. Step

1. Stating the problem: We are given a square with diagonals of length 10 cm and need to find the length of each side of the square. 2. Recall that in a square, the diagonals are e

1. We are asked to find the length of the diagonal of a rectangle with length $9$ cm and width $4$ cm. 2. Recall that the diagonal $d$ of a rectangle can be found using the Pythago

1. **Stating the problem:** We have a circle with points X, Y, and Z on its circumference. Angle at point X is 146°, angle at point Y is 110°, and angle at point Z is unknown. We n

1. **Problem restatement:** Given a circle with points Y, Z, and X on its circumference, the angles at Y and X are 110° and 146°, respectively. We need to find the unknown angle at

1. مسئلہ: مثلث کے زاویوں کے نصف ہوتے ہیں، مثلث کی زاویوں کی ترچھی لکیریں (Bisectors) کیا خصوصیت رکھتی ہیں؟ تمام مثلث کی زاویوں کی ترچھی لکیریں ایک نقطے پر ملتی ہیں جسے مثلث کا اندر

1. Problem: Find the area and perimeter of the L-shaped polygon with vertical sides 10 cm and 8 cm, and horizontal sides 18 cm and 8 cm. 2. Breakdown the L-shape into two rectangle

1. Problem Q1: The longer leg of a right triangle is 4 cm more than the shorter leg and the hypotenuse is 20 cm. 2. Let the shorter leg be $x$ cm, so the longer leg is $x+4$ cm.

1.\ \text{المطلوب هو فهم العلاقة بين:}\ \text{الوتر } SQ=\sqrt{7},\ \text{نصف القطر } r,\ \text{والزاوية } \theta,\ \text{ وأيضًا المتجهات أو الخطوط المرسومة.}\ \newline 2.\ \text

1. State the problem: Solve for $r$ in the equation $$r^2 + (r + 5)^2 = 17^2.$$\n\n2. Expand the squared binomial: $$(r + 5)^2 = r^2 + 2 \cdot r \cdot 5 + 5^2 = r^2 + 10r + 25.$$\n

1. **بيان المشكلة:** لدينا دائرة نصف قطرها $q$، مع وجود مثلث خارجي يشمل نقطة $p$، ومتجهة عن الدائرة بخط مسماه $u$. الزاوية بين هذا الخط والوتر الدائري هي $30^{\circ}$. 2. **الهدف:*

1. **State the problem:** We need to find the length of a rectangular park given that the breadth is 19 meters and the area is 665 square meters. 2. **Recall the formula for the ar

1. **Stating the problem:** We have a triangle with vertices A, B, and Target. Side AB measures 14.5 meters. Angle at A is 96° and angle at B is 58°. We want to find the length of

1. To find the area, first identify the shape or the region to be measured. 2. If it's a geometric shape, use the appropriate area formula, for example, for a rectangle area $= \te

1. **Énoncé du problème** : Vérifier que le plan \( (P) : x + y + 2z - 2 = 0 \) est déterminé par les trois points \( A(1 ; 1 ; 0), B(2 ; 0 ; 0), C(1 ; 3 ; -1) \). 2. **Calculer le

1. Let's consider the problem about triangles. Since no specific problem is given, we'll review the general properties of triangles and how to find the area. 2. A triangle is a pol

1. **Problem statement:** We are given points $A(1,1,0)$, $B(2,0,0)$, $C(1,3,-1)$, and $E(2,2,2)$. **a. Find the equation of plane $(P)$ determined by points $A$, $B$, and $C$.**

1. **Problem statement:** Find the volume of a triangular prism with base sides 3 cm, 4 cm, and 5 cm, and height 10 cm. 2. The triangle with sides 3, 4, and 5 is a right triangle (

1. **State the problem**: We need to find the three-figure bearings from the centre to Town A and Town C based on given angles. 2. **Understand bearings**: Bearings are measured cl

1. Problem statement: We want to find the shortest length of a bridge connecting two islands. The first island is shaped like a parabola with height 4 km, and the second is a circl

1. State the problem: Find the obtuse angle that the line segment AB forms with the x-axis, where A = $(4,-3)$ and B = $(8,5)$.\n2. Calculate the slope of line AB using the formula