📐 geometry

1. **State the problem:** We are given the measure of an exterior angle of a regular polygon as 18 degrees. We need to find the measure of an interior angle and the number of sides

1. **Problem:** Find the volume of a cylinder with radius $r=11$ m and height $h=22$ m. 2. **Formula:** The volume $V$ of a cylinder is given by

1. **State the problem:** We need to find the coordinates of triangle \(\triangle DEF\) after a rotation of 270° clockwise around the origin. The original vertices are \(D(-9,-7)\)

1. Problem: Find the scale factor for a model car 12 inches long representing a 192-inch-long car. 2. Formula: Scale factor = \frac{Model\ length}{Actual\ length}

1. Problem 9: The hour hand on a clock is 12 cm long. What area does it pass over in 5 h? Take π as 3.14. 2. Formula: Area of sector = $$\frac{\theta}{360} \times \pi r^2$$ where $

1. **State the problem:** Find the exterior angle sum of a polygon with 500 sides (a 500-gon). 2. **Formula and rule:** The sum of the exterior angles of any polygon, regardless of

1. **Problem statement:** Calculate the perimeter of a compound shape formed by a rectangle and a sector of a circle. 2. **Given:**

1. The problem asks to determine the relationship between lines AC and RS based on the given diagram and information. 2. Important definitions:

1. The problem asks to find the measure of angle $\angle CED$ given in the figure. 2. From the problem statement, the measure of $\angle CED$ is directly given as 122 degrees.

1. The problem asks to identify which two statements about perpendicularity (\(\perp\)) and parallelism (\(\parallel\)) between vectors are both true. 2. Recall the definitions:

1. **State the problem:** Determine the relationship between lines a and d based on the given diagram and options. 2. **Analyze the diagram:**

1. **Stating the problem:** We have an L-shaped figure made of two rectangles. The horizontal rectangle has width 7 m and length 20 m. The vertical rectangle has width 7 m and leng

1. Problem 14: Calculate the area of a triangle with sides 17.1 cm, 22.8 cm, and 28.5 cm. 2. We use Heron's formula for the area of a triangle when all three sides are known:

1. **State the problem:** We have a triangle RST with sides RS = $3x + 4$ and RT = $8x + 4$. The angle between the extension of JR and RT is 140°. We want to find the value of $x$.

1. **State the problem:** We need to find the surface area of a right rectangular prism with dimensions 11 m, 7 m, and 13 m. 2. **Formula for surface area of a rectangular prism:**

1. **State the problem:** We need to find the total surface area of a cube with side length 19 cm, which represents the amount of wrapping paper used. 2. **Formula:** The surface a

1. **Problem Statement:** Rotate the triangle with vertices at $A(2,2)$, $B(4,2)$, and $C(4,4)$ by 90° clockwise about the origin. 2. **Formula for 90° Clockwise Rotation:**

1. **Problem Statement:** Reflect the triangle with vertices at $A(0,-4)$, $B(2,-4)$, and $C(2,-6)$ over the vertical line $p$ given by $x = -2$. 2. **Reflection Formula:** For a p

1. The problem asks for the coordinates, but we need more context to determine which coordinates are required. 2. Coordinates usually refer to points in a plane or space, often giv

1. **Problem Statement:** Reflect the triangle with vertices at $ (2, -4), (4, -2), (4, -4) $ over the vertical line $ p $, which is the y-axis ($ x=0 $). 2. **Reflection Rule:** W

1. **Problem statement:** Reflect the quadrilateral with vertices at $(-7,1)$, $(-6,4)$, $(-3,3)$, and $(-3,0)$ across the vertical line $n$ which is the $y$-axis ($x=0$). 2. **Ref