📐 geometry

1. **Stating the problem:** We have a square with side length 8 units and four quarter circles of radius 8 units centered at each corner of the square. We want to understand the sh

1. **Problem statement:** We need to find the volume of a triangular prism where the base triangle has sides and angles given, including angle $\angle BDE = 25^\circ$, base length

1. **State the problem:** We need to find the volume of a triangular prism where the base is triangle ABD with right angle at B, and the prism height is along edge DE. Given: $\ang

1. **Problem statement:** We need to calculate the volume of the triangular prism where angle $BDE = 22^\circ$, $BD = 59$ m, and $AD = 27$ m. The prism has right angles at $B$ and

1. **State the problem:** We have a trapezium with top base $x+4$ cm, bottom base $x+2$ cm, height $x-1$ cm, and area 32 cm$^2$. We need to find the value of $x$. 2. **Formula for

1. **Problem Statement:** Given circle ⊙X with points A, B, C, D, E, F on the circumference and angles $m\angle AF = 32^\circ$, $m\angle DAC = 26^\circ$, and $m\angle BXD = 126^\ci

1. **Stel die probleem:** Ons het 'n parallelogram ABCD met punte A(-2, -6), B(4, 0), C(-1, 10) en D(x, y). Ons moet verskeie eienskappe bereken. 2. **Bereken die lengte van BC:**

1. **State the problem:** We have a circle centered at point A.

1. **Problem Statement:** In circle A, diameter BE = 10 bisects chord CD = 6, and arc CD = 90 degrees. Find the measure of arc DE, line FD, and line AF.

1. **Problem Statement:** We have a circle with diameter BE = 10, chord CD = 6, and arc CD = 90 degrees. We need to find the measure of arc DE, length of line FD, and length of lin

1. **Problem Statement:** Given a circle with diameter $BE = 10$, chord $CD = 6$ is bisected by $BE$, and arc $CD$ measures $90^\circ$. We need to find the measure of arc $DE$, len

1. **Problem Statement:** Identify the figure in which angles $B_1$ and $B_2$ are complementary. 2. **Definition:** Complementary angles are two angles whose measures add up to $90

1. The problem is to understand the meaning of "complementary" in mathematics. 2. In mathematics, "complementary" usually refers to two angles whose measures add up to 90 degrees.

1. The problem is to draw a quadrilateral with side lengths 2, 3, 4.5, 2 and a diagonal of length 6. 2. A quadrilateral has four sides, but you provided five measurements. Likely,

1. The problem is to draw a quadrilateral with side lengths 3, 4, 4.5, 2 and a diagonal of length 6. 2. A quadrilateral has four sides, so the given five measurements likely includ

1. **Problem Statement:** We need to find the radius of a cylindrical container given its height is 12 inches. 2. **Formula Used:** The volume $V$ of a cylinder is given by the for

1. **State the problem:** We are given a rectangular prism container with a height of $11 \frac{1}{2}$ inches and a length of $7 \frac{1}{2}$ inches. We need to find the width of t

1. The problem involves a sequence of geometric transformations on shapes A, P, M, and others, including reflections, translations, and rotations. 2. For problem 7, we start with s

1. **Problem statement:** We need to find the volume of a wedge cut from a circular cylinder of radius 4 by two planes. One plane is perpendicular to the cylinder's axis, and the o

1. **Stating the problem:** You are asked to identify types of transformations (translation, reflection, rotation) applied to geometric figures on grids and describe combined trans

1. **State the problem:** We need to find the total area of a composite shape consisting of a rectangle and a right triangle. 2. **Identify the shapes and their dimensions:**