📐 geometry

1. **State the problem:** We need to find the length $VT$ in kite $RUST$ where diagonals $RT$ and $US$ intersect at $V$ at a right angle. 2. **Given information:**

1. **State the problem:** We have two similar right triangles, a large one with sides 10, 6, and 11.661904, and a smaller one with sides 2.5, 1.5, and 2.9154759. We need to find th

1. **State the problem:** We need to find the total volume of a 3D figure made up of small cubes, each with a volume of 1 mm^3. 2. **Understand the volume formula:** The volume of

1. **State the problem:** Find the volume of a rectangular prism with dimensions 4 units by 3 units by 2 units. 2. **Formula:** The volume $V$ of a rectangular prism is given by th

1. **State the problem:** We need to find which set of dimensions forms a rectangular prism with a volume of 99 cubic inches. 2. **Formula for volume of a rectangular prism:**

1. **State the problem:** We need to find the volume of a sphere with radius $r = 1$ ft. 2. **Formula for the volume of a sphere:**

1. **State the problem:** We need to find the volume of a sphere with radius $r = 7$ meters. 2. **Formula for the volume of a sphere:**

1. The problem asks whether Jan's statement is correct: "A rhombus is a parallelogram and every parallelogram is also a rhombus." 2. First, recall definitions:

1. **Stating the problem:** Jan claims that a rhombus is a parallelogram and that every parallelogram is also a rhombus. 2. **Definitions and properties:**

1. **Problem Statement:** Find the volume and surface area of a triangular prism with base triangle dimensions base = 8 ft, height = 5 ft, prism length = 14.2 ft, and another edge

1. **State the problem:** We have two concentric circles (same center). The inner circle has diameter $d=51.8$ miles, and the outer circle has radius $r=13.2$ miles. We need to fin

1. **State the problem:** We need to find the area of a compound polygon composed of rectangles and a triangle with given side lengths. 2. **Identify the shapes and dimensions:** T

1. **State the problem:** Find the surface area of a triangular prism with given side lengths 15 yd, 12 yd, 13 yd, and 9 yd. 2. **Identify the shape and dimensions:** The prism has

1. **State the problem:** Find the perimeter of triangle $\triangle GHI$ given sides $HG=27.5$, $IG=21$, and angles $\angle H=49^\circ$, $\angle G=48^\circ$. Side $HI=x$ is unknown

1. **State the problem:** We are given the side lengths of triangle $NOP$ as $PN=68$ and $ON=55.2$. We need to find the perimeter of triangle $NOP$, which is the sum of all its sid

1. **State the problem:** We are given rectangle PSRV with sides PS = 9 ft and SR = 3 ft. We need to find the length of side VR. 2. **Recall properties of rectangles:** Opposite si

1. The problem asks for the scale factor and center of dilation given two similar pentagon-like figures, one larger (D, E, F, G, I) and one smaller (D', E', F', G', H', I'). 2. The

1. **State the problem:** We have a triangle with vertices at points $(3, 2)$, $(7, 2)$, and $(3, 6)$. We want to reflect this triangle over the $y$-axis and find the new coordinat

1. **State the problem:** Find the distance between the points $(8, 7)$ and $(-2, 10)$. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given b

1. **State the problem:** We need to approximate the volume of a sphere with radius $r = 4.8$ mm. 2. **Formula:** The volume $V$ of a sphere is given by the formula:

1. **State the problem:** We need to approximate the volume of a sphere with radius $r=2$ inches. 2. **Formula for the volume of a sphere:**