📐 geometry

1. **Problem statement:** Find (a) the length CD in terms of r and sin \(\theta\), (b) the perimeter of sector CAB given \(r=4\) and \(\theta=\frac{1}{6}\pi\), and (c) the area of

1. **Problem statement:** Given rectangle ABCD with AB > BC, line xy passes through B and is parallel to diagonal AC. Line xy intersects AD at point E. Prove that quadrilateral ACB

1. The problem asks to plot the points (-2,1), (0,3), (3,0), and (3,5) on the Cartesian coordinate system. 2. Each point is represented as $(x,y)$ where $x$ is the horizontal coord

1. **Problem Statement:** Given a parallelogram ABCD with diagonals intersecting at O, points P and Q are midpoints of AO and BC respectively. Given that $\angle A = \angle DPO$ an

1. مسئله: اندازه پاره‌خط AB در دایره مثلثاتی برابر $\sqrt{3} + \sqrt{2}$ است. نقطه A روی محور طول‌ها (محور x) در سمت منفی قرار دارد و نقطه B روی محیط دایره در ربع اول است. هدف یافت

1. The problem is to find the volume of a prism. 2. The formula for the volume of a prism is $$V = B \times h$$ where $B$ is the area of the base and $h$ is the height of the prism

1. The problem is to understand what a prism is in geometry. 2. A prism is a solid geometric figure with two parallel, congruent bases connected by rectangular faces.

1. The problem is to find the volume of a solid. 2. To find volume, we need to know the shape and its dimensions. Common formulas include:

1. The problem involves finding the area of a trapezoidal cross-section with top width $4.8$ m, bottom width $1.2$ m, and height $1.5$ m. 2. The formula for the area $A$ of a trape

1. **Stating the problem:** We have a trapezoidal prism with the trapezoid base having top side $4.8$ meters, bottom side $1.2$ meters, and height $1.5$ meters. We want to find the

1. The problem asks to solve the 2nd question of the given figure, but since the figure is not provided, I will explain how to approach a typical 2nd question in math problems invo

1. The problem asks to match each polar coordinate point $(r, \theta)$ with one of the labeled points A, B, C, or D on the graph. 2. Recall that in polar coordinates, a negative ra

1. **Problem 8:** \(\angle A\) is obtuse and \(\angle A = (x + 20)^\circ\). Find the limits of \(x\). - An obtuse angle is greater than 90° and less than 180°.

1. **Stating the problem:** We have two parallel lines PQ and RS cut by a transversal XY. We need to identify corresponding angles and find the values of angles \(\angle a\) and \(

1. The problem involves finding unknown angles at points q, f, and b based on given angles around those points. 2. For point q, the sum of angles around a point is 360°. Given two

1. **State the problem:** We need to find the length of the midsegment $RT$ in trapezoid $ZRWX$ where $ZR$ and $WX$ are the parallel sides. 2. **Recall the midsegment formula for t

1. ปัญหา: เขียนเวกเตอร์ $\overrightarrow{EG}$ ในรูปของเวกเตอร์ $\mathbf{\bar{u}} = \overrightarrow{BA}$ และ $\mathbf{\bar{v}} = \overrightarrow{CB}$ ในรูปสี่เหลี่ยมด้านขนาน ABCD โด

1. The problem is to construct an angle \(\angle AOB\) such that \(\angle AOB = 45^\circ\). 2. To create a 45-degree angle, we use the fact that 45 degrees is half of 90 degrees, w

1. **Problem:** Label the sides of a right triangle with vertices P (top), Q (bottom-left, right angle), and R (bottom-right). State the Pythagorean theorem as it applies to these

1. The problem asks to find the surface area $SA$ of a sphere given its volume $V=880$ ft$^3$. The formula for surface area is: $$SA = 4\pi \left(\frac{3V}{4\pi}\right)^{\frac{2}{3

1. The problem asks to find the radius $r$ of a sphere given its volume $V = 904.8$ cm$^3$ using the formula: $$r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$$