📐 geometry

1. The problem is to determine how to arrange 10 small boxes inside one larger box. 2. This is a spatial arrangement problem, often solved by considering dimensions and packing.

1. **State the problem:** We have two similar triangles CDE and FGH. We know sides CD = 14, CE = 23, and side HG = 57. We need to find the length of side FG. 2. **Recall the proper

1. **State the problem:** We need to find the radius $r$ of a hemisphere given its volume $V = 78100$ cm$^3$. 2. **Formula for volume of a hemisphere:** The volume of a full sphere

1. **State the problem:** We have two cylinders, A and B. Cylinder A has radius $3.5$ cm and height $7.4$ cm and is $40\%$ full of liquid. The liquid is poured into cylinder B, whi

1. **State the problem:** We are given a midpoint of a line segment and one endpoint, and we need to find the other endpoint. 2. **Formula used:** The midpoint $M$ of a segment wit

1. The problem is to identify and understand the coordinates of points plotted on a coordinate plane. 2. Each point is given as an ordered pair $(x, y)$ where $x$ is the horizontal

1. The problem asks to determine the ordered pairs for each point in the table using the given grid points. 2. The ordered pair for a point is written as $(x, y)$ where $x$ is the

1. **State the problem:** We have a rectangle SUVW with area 40 sq cm and a parallelogram RTWX adjacent to it. We need to find the area of the parallelogram RTWX. 2. **Given data:*

1. **Problem statement:** We have a kite-shaped quadrilateral WXYZ with diagonals WY and XZ intersecting at U. 2. **Given:** WY is divided into two segments 12 and 12 by U, so WY =

1. **State the problem:** We have two similar triangles. In the first triangle, angles $\angle L = 55^\circ$ and $\angle J = 100^\circ$ are given. We need to find the measures of a

1. The problem asks to find the perimeter of the given image. 2. The perimeter of a polygon is the sum of the lengths of all its sides.

1. **State the problem:** We need to find the length of segment $YX$ in kite $WXYZ$. 2. **Recall kite properties:** In a kite, two pairs of adjacent sides are equal. Here, $WX = XY

1. **State the problem:** We need to find the value of the unknown angle $x^\circ$ in a figure where angles 43°, 42°, and 120° are given along a horizontal line. 2. **Understand th

1. **State the problem:** We need to find the perimeter of kite WXYZ. 2. **Recall the formula:** The perimeter $P$ of a kite is the sum of the lengths of all its sides. Since a kit

1. **State the problem:** We have kite quadrilateral $WXYZ$ with diagonals intersecting at $U$. Given lengths are $WU=12$, $UY=12$, $XU=6$, and $UZ=24$. We need to find the length

1. **Problem statement:** We have kite $WXYZ$ with angles $m\angle W = 74^\circ$ and $m\angle Y = 56^\circ$. We need to find $m\angle Z$. 2. **Recall kite properties:** In a kite,

1. **State the problem:** We need to find the measure of angle $\angle T$ in trapezoid $TVYZ$ where $TY \cong VZ$ and $TV \parallel YZ$. Given $\angle V = 60^\circ$. 2. **Recall pr

1. **State the problem:** We have triangle LMN with vertices L(1, -2), M(3, 0), and N(2, -3). We want to find the coordinates of the dilated triangle L'M'N' after a dilation with s

1. **Problem:** \nGiven that \(\angle 1\) and \(\angle 2\) are vertical angles, and \(m\angle 1 = (5x + 12)^\circ\), \(m\angle 2 = (6x - 11)^\circ\), find \(m\angle 1\).\n\n2. **Ru

1. **State the problem:** We need to find the range of possible lengths for the third side $n$ of a triangle when the other two sides measure 6 ft and 19 ft. 2. **Recall the triang

1. **State the problem:** Determine if a triangle can be formed with side lengths 0.7, 1.4, and 2.1. 2. **Recall the Triangle Inequality Theorem:** For any triangle with sides $a$,