📐 geometry

1. **Problem statement:** Calculate the area of trapezium ABCD where:

1. **Problem statement:** We have a right triangle GHD with a right angle at H. The hypotenuse GD is 18 units, side GH is 14 units, and we need to find the length HD. 2. **Identify

1. **Stating the problem:** We need to find the area of a trapezium (trapezoid) with given side lengths and angles. 2. **Given data:**

1. **Problem Statement:** Define the four boundary lines of a recreational park given its coordinates and label them on a coordinate grid. 2. **Understanding Boundary Lines:** Boun

1. The problem is to find the coordinates of the recreational area. 2. Since the problem statement is incomplete and does not provide any specific information or data about the rec

1. Problem: Find the length of the hypotenuse in a right triangle using the Pythagorean theorem. 2. The Pythagorean theorem states that in a right triangle, the square of the hypot

1. The problem states that $R$ is the radius of a circle. 2. The radius $R$ is the distance from the center of the circle to any point on its circumference.

1. The problem is to understand what the big $R$ and small $r$ represent in the context of circles. 2. In geometry, when dealing with circles, the letter $R$ often denotes the radi

1. The problem is to understand what the symbol $h$ means in the context of a trapezoid (trapezium). 2. In geometry, a trapezoid is a quadrilateral with at least one pair of parall

1. **State the problem:** We have two triangles with vertical segments inside them. We need to find the value of $x$ and then calculate the length of segment $VT$ in the second tri

1. **Problem Statement:** We have two similar triangles, $\triangle ABC$ and $\triangle BDE$. We know $DE=10$ cm, and the side lengths at vertices are $AB=6$, $BC=8$, and $AC=5$. W

1. **Problem Statement:** We are given two similar triangles, $\triangle ABC$ and $\triangle BDE$. We need to determine if the areas of $\triangle ABL$ and $\triangle ALC$ are equa

1. **Problem Statement:** We have a cyclic quadrilateral ABCD inscribed in a circle with diagonals AC and BD intersecting at point E. Given angles \(\angle A = 25^\circ\) and \(\an

1. **Problem Statement:** A chord of length 16 cm is drawn in a circle with radius 10 cm. We need to find the distance from the center of the circle to the chord.

1. **Problem statement:** We have an isosceles triangle ABC where sides AB and BC are equal in length, and side AC is parallel to the x-axis. We need to find the coordinates of poi

1. **State the problem:** We have an isosceles triangle ABC with AB = BC and side AC parallel to the x-axis. Points B and C are given as B(10, 8) and C(16, 2). Point A lies on the

1. **State the problem:** We are given a rectangle DEFG with center C at coordinates (8, 7) and point E at (20, 25). We need to find the coordinates of point G. 2. **Recall propert

1. **State the problem:** We need to find the coordinates of the center, C, of a rectangle given its bottom-left corner at $ (8, -4) $ and top-right corner at $ (16, 10) $. 2. **Fo

1. **Problem statement:** We have a pentagon DEFGH with a vertical line of symmetry at $x=7$. Points E, F, and G have coordinates $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to fi

1. **Problem Statement:** We have a pentagon DEFGH symmetric about the vertical line $x=7$. Given points are $E(7,10)$, $F(11,8)$, and $G(12,0)$. We need to find coordinates of $D$

1. **Problem Statement:** Given a parallelogram ABCD with points A(-11, 23), B(-13, 29), and C(5, 22), find the coordinates of point D. 2. **Formula and Concept:** In a parallelogr