📐 geometry

1. **State the problem:** Riley and Anthony run around a semi-circular curve. Riley runs on the inside lane with radius $35$ meters, and Anthony runs on the outside lane with radiu

1. **State the problem:** We need to find the length of a rectangular prism given its volume and two dimensions: height and width.

1. **State the problem:** We need to find how much area of the room will NOT be covered by the rug. 2. **Identify given information:** From the image annotations, the room's total

1. **Problem statement:** We have four rectangles A, B, C, and D, all with the same perimeter. We need to order them from greatest to least area. 2. **Formula and rules:** The peri

1. **Stating the problem:** Find the length of the hypotenuse $x$ of a right triangle where one leg is the radius of a circle with length 6, and the other leg outside the circle is

1. **Stating the problem:** We have a circle with radius 6, and a triangle formed by a radius, a segment outside the circle labeled 8, and the hypotenuse labeled $x$. We need to fi

1. **State the problem:** We have a large triangle composed of smaller triangles with given angles 40°, 30°, and 50°, and we need to find the unknown angle marked with a question m

1. **State the problem:** We need to find the perimeter of a rectangular rug with dimensions 6.25 feet by 8.5 feet. 2. **Formula for perimeter of a rectangle:**

1. **State the problem:** Calculate the volume of a trapezoidal prism with the following dimensions:

1. **State the problem:** We need to find the image of triangle \(\Delta TUV\) after reflecting it over the y-axis. 2. **Recall the reflection rule:** Reflecting a point \((x, y)\)

1. **Problem statement:** Given that FH bisects \(\angle EFG\), and the segments \(EF = 9x + 9\) and \(FG = 12x - 3\), find the measure of \(\angle EFH\). 2. **Understanding the pr

1. **State the problem:** We need to find the value of $n$ in a triangle with angles $(n + 17)^\circ$, $31^\circ$, and $75^\circ$. 2. **Recall the triangle angle sum rule:** The su

1. The problem asks to find the image of triangle UVW after reflecting it over the x-axis. 2. Reflection over the x-axis changes the y-coordinate of each point to its opposite, whi

1. **State the problem:** We are given two adjacent angles on a straight line, labeled $(-7y + 97)^\circ$ and $(3y + 75)^\circ$, and we need to find the value of $y$. 2. **Use the

1. **State the problem:** We need to find the radius of a circle given its circumference is $45\pi$ centimeters. 2. **Formula used:** The circumference $C$ of a circle is related t

1. **State the problem:** We are given a semicircle with radius $2$ and want to understand its properties. 2. **Formula for a circle:** The equation of a circle centered at the ori

1. **Problem statement:** Find the perimeter and area of a composite figure consisting of a rectangle, a quarter circle on the left, and a semicircle on the right. 2. **Given dimen

1. **State the problem:** Find the diameter of a circle given its area is 415.48 square inches. 2. **Formula used:** The area $A$ of a circle is given by the formula $$A = \pi r^2$

1. **State the problem:** Given triangle $\triangle WXY$ with $m\angle X = 15^\circ$, $m\angle Y = 20^\circ$, and side $WY = 7.5$, find all sides and angles. 2. **Find the missing

1. **Stating the problem:** We are given two triangles, $\triangle XYZ$ and $\triangle RYS$, which are similar, denoted as $\triangle XYZ \sim \triangle RYS$. 2. **Understanding si

1. **Problem:** Find the measure of angle A in triangle ABC where angles are given as $4x + 5$, $5x$, and $6x + 10$. 2. **Formula:** The sum of interior angles in a triangle is alw