📐 geometry

1. **State the problem:** We need to find the volume of a cylinder with diameter $6$ cm and height $50$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by the formula:

1. **Problem 2: Find the missing leg in a right triangle with hypotenuse 15 and one leg 8.** 2. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse.

1. **State the problem:** We are given the equation $x + 38 + 90 = 180$ and need to solve for $x$. 2. **Use the angle sum property of a triangle:** The sum of the interior angles o

1. **State the problem:** We are given a rhombus STUV with points S(-1,4) and T(6,4). We need to find the length of side TU. 2. **Recall properties of a rhombus:** All sides of a r

1. **State the problem:** Given rectangle ABCD with angles at vertices B and C expressed as $(2x + 10)^\circ$ and $(3x - 30)^\circ$ respectively, find the value of $x$. 2. **Recall

1. **State the problem:** We need to find the number of sides of a polygon whose sum of interior angles is 3600°. 2. **Formula:** The sum of interior angles $S$ of a polygon with $

1. **State the problem:** We are given a rhombus ABCD with $m\angle DAB = 110^\circ$. We need to find the measures of all angles in the rhombus and the angles $m\angle DEA$ and $m\

1. **Stating the problem:** We have a trapezoid with bases of lengths $a$ (top) and 46 (bottom). The lower left angle is $60^\circ$, the lower right angle is $55^\circ$, and a segm

1. **State the problem:** We have a parallelogram with angles labeled $y^\circ$, $47^\circ$, $x^\circ$, and one angle given as $38^\circ$. We need to find the value of $y$. 2. **Re

1. **State the problem:** We need to find the value of $x$ given that the exterior angle of a regular octagon is $(4x - 3)^\circ$. 2. **Recall the formula for exterior angles of re

1. **Problem Statement:** We have a regular hexagon ABEFGH and a regular quadrilateral BCDE sharing the edge BE. We need to find the measure of angle $\angle DEF$. 2. **Key Propert

1. **State the problem:** We are given a trapezoid BADC with bases BC = 12 cm and AD = 26 cm. We need to find the length of the median EF, where EF is parallel to the bases and con

1. **State the problem:** We have a parallelogram ABCD with points A(0,0), B(2,4), and C(10,4). We need to find the coordinates of point D. 2. **Formula and rule:** In a parallelog

1. **State the problem:** We need to find the actual area of Bedroom 1 from a scale drawing where 1 inch represents 3 feet. 2. **Given:** Bedroom 1 measures 3 1/2 inches by 3 1/2 i

1. **Problem:** Find the perimeter and area of the rectangle shown in the figure. 2. **Given:** Length $l = 8$ units, Width $w = 5$ units.

1. The user asks if I can generate images like geometrical figures to find areas. 2. Yes, I can generate SVG images of geometric figures to help visualize and solve area problems.

1. The problem states a circle with equation $$(x - 2)^2 + (y - 4)^2 = 20$$ and asks if the point $(6, 6)$ lies on, inside, or outside the circle. 2. The general form of a circle's

1. **Problem Statement:** We are given a circle centered at point A with coordinates $(5, -1)$ and a point B on the circle at coordinates $(5, 1)$. We need to find the radius of th

1. **State the problem:** We are given two similar quadrilaterals $WXYZ \sim FIHG$ and some side lengths. We need to find the lengths of segments $GH$ and $WX$. 2. **Identify corre

1. **State the problem:** We have two similar polygons WXYZ and FIHG. We know some side lengths and need to find $GH$ and $WX$. 2. **Identify known sides:**

1. **State the problem:** We have a circle with radius $5$ cm. We want to find the length of arcs corresponding to angles of $1$ radian and $2.2$ radians.