📐 geometry

1. **State the problem:** We have a circular storm drain pipe partially filled with water. The chord length across the water surface is 48 inches, and the water depth (distance fro

1. **State the problem:** Show that quadrilateral WXYZ with vertices W(1,4), X(1,8), Y(-3,9), Z(-3,3) is a trapezoid and decide if it is isosceles. 2. **Recall the trapezoid defini

1. **State the problem:** Find the area of a figure composed of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Given dimensions:** Rectangle l

1. **State the problem:** We need to find the area of a figure composed of a square with side length 8 and four semicircles attached to each side, each with diameter 8. 2. **Formul

1. **State the problem:** Given that \overline{WZ} is the perpendicular bisector of \overline{VY}, we need to determine which angle congruence conclusion is correct. 2. **Recall th

1. **Problem statement:** We have a triangle with angles near vertex S labeled as $(2x + 24)^\circ$ and $30^\circ$, and segments $TQ \cong QR$. We need to find the value of $x$. 2.

1. **Stating the problem:** We have a triangle with vertices at (0,0), (1,0), and (1,1). The sides are labeled as base $b$, height $a$, and hypotenuse $c$. The problem states the f

1. The problem involves identifying the coordinates of points on a coordinate grid. 2. The coordinate grid has x and y axes ranging from -5 to 5.

1. **Stating the problem:** We have a right triangle HJT with angles 60°, 30°, and 90° at T. The sides are labeled as follows: HJ = 2x (hypotenuse), HT = x (shorter leg), and TJ =

1. **Problem statement:** We have a quadrilateral ABCD with right angles at points C and A. Given lengths are BC = 19 m, CD = 10 m, and AB = 14 m. We need to find the length AD. 2.

1. **Problem Statement:** Find the coordinates of point $U$ which partitions the segment $WB$ proportionally. Given points:

1. The problem asks us to find the equation of a circle given its center and radius. 2. The standard form of a circle's equation is $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h, k)$

1. **Problem Statement:** Find the coordinates of point U given points Z(-4,0), G(-4,-6), and C on segment ZG such that C divides ZG in a certain ratio, and U lies on a line from C

1. **Problem:** Find the missing side length in triangle 1a with sides 12 cm and 8 cm. 2. **Formula:** Use the Pythagorean theorem for right triangles or the Law of Cosines for any

1. **Problem statement:** We have a net of a rectangular pyramid with a diamond shape split into four triangles by two perpendicular dashed lines. The vertical dashed line is 11 yd

1. **Problem Statement:** Find the surface area of a square pyramid given its net. The net consists of a square base with side length 10 m and four congruent triangular faces each

1. **State the problem:** We are given the area of a circle as $36\pi$ square inches and need to find the circumference in terms of $\pi$. 2. **Recall formulas:**

1. **State the problem:** We need to find the volume of a rectangular prism with side lengths $\frac{3}{4}$ cm, $\frac{1}{5}$ cm, and $\frac{5}{7}$ cm. 2. **Formula for volume of a

1. **Problem statement:** Two parallel lines $u$ and $v$ are cut by a transversal $f$. Given $m \angle 1 = 70^\circ$, find the measures of angles 2 and 3 and identify their relatio

1. **State the problem:** Calculate the volume of a rectangular prism with length $14$ ft, width $9$ ft, and height $5$ ft. 2. **Formula:** The volume $V$ of a rectangular prism is

1. The problem asks to find the lines of symmetry for a regular hexagon and select all that apply from lines l, m, n, and o. 2. A regular hexagon has 6 lines of symmetry: 3 lines p