📐 geometry

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: $$r = \left(\frac{3V}{4\pi}\right)^{\frac{1}{3}}$$

1. **State the problem:** We need to find the radius $r$ of the base of a cone given the height $h=6$ inches and volume $V=464.7$ cubic inches. 2. **Given formula:**

1. **Problem statement:** We have a triangle with a perpendicular height of 12 units. The base is divided into two segments: one segment is $x$ and the other is 16. We want to find

1. **State the problem:** Ella and Jake built a ramp frame shaped like a rectangular prism with a triangular side. We need to find the total surface area of the ramp, including the

1. **State the problem:** We need to find the area of a trapezoid with one pair of parallel sides. 2. **Identify the bases and height:** The trapezoid has a bottom base divided int

1. **State the problem:** We need to find the area of a parallelogram with a base of 15 units and a height of 9 units. 2. **Formula for the area of a parallelogram:**

1. The problem is to construct the bisector of \(\angle DEF\).\n\n2. The angle bisector divides the angle into two equal parts. To construct it, use a compass to draw arcs from ver

1. **State the problem:** Given a triangle ABC with $AB \perp AC$, $DE \perp FG$, $CD \cong CE$, and $m\angle B = 44^\circ$, find $m\angle FGB$. 2. **Given information:**

1. Énoncé du problème : Nous avons un triangle ABC rectangle en A, avec AB = \sqrt{3} et \tan \hat{B} = \sqrt{2}.