📐 geometry

1. The problem is to graph a circle. 2. The standard formula for a circle centered at the origin with radius $r$ is:

1. **State the problem:** We have a right triangle with three sides: shorter leg, longer leg, and hypotenuse. The longer leg is 3 cm more than three times the shorter leg.

1. **Problem statement:** Find the total area of each rectangle given the areas of smaller rectangles inside and the lengths of portions of the sides. 2. **Rectangle a:**

1. **State the problem:** Find the area of a rectangle with length 3 feet and width \(\frac{1}{4}\) foot. 2. **Formula:** The area \(A\) of a rectangle is given by \(A = \text{leng

1. The problem asks to find the matching counterclockwise angle for given clockwise angles 175° and 285°. 2. Important rule: A full circle is 360°. Clockwise and counterclockwise a

1. **Problem Statement:** Calculate the volume of water in a pool with given dimensions where water is filled to 9 feet from the top.

1. **Problem Statement:** Determine the image of point $P(-6,4)$ after reflection over the line $y+x=0$, which can be rewritten as $y=-x$.

1. **State the problem:** We need to translate triangle P by the vector $(2, -7)$. This means moving every vertex of the triangle 2 units to the right and 7 units down. 2. **Vertic

1. **Problem:** Find the perimeter of the house in terms of $c$. 2. **Formula:** The perimeter of a polygon is the sum of the lengths of all its sides.

1. **State the problem:** We are given a triangle with two sides measuring 6 mm and 16 mm, and the angle between them is $\theta = 14.4^\circ$. We need to find the area of this tri

1. **State the problem:** Calculate the surface area of a cone with radius $r=7$ cm and height $h=12$ cm. 2. **Formula:** The surface area $A$ of a cone is given by

1. **Problem Statement:** We need to find the image of square JKLM after a 90° counterclockwise rotation around the origin. 2. **Vertices of the original square JKLM:**

1. **State the problem:** We need to find the image of trapezoid EFGH after a 180° counterclockwise rotation around the origin. 2. **Recall the rotation formula:** A 180° rotation

1. **Problem Statement:** We need to find the image of rectangle TUWV after a 180° counterclockwise rotation about the origin. 2. **Vertices of the original rectangle:**

1. **Problem Statement:** We are given a triangle SRT with angles at vertices R and T expressed as $(3x + 1)^\circ$ and $(2x + 2)^\circ$ respectively. The sides SR and ST are congr

1. The problem involves understanding four key topics in Grade 8 math: Geometry of Straight Lines, Geometry of 2D Shapes, The Theorem of Pythagoras, and Area and Perimeter of 2D Sh

1. **Problem Statement:** Identify which of the given arcs is a minor arc on the circle. 2. **Definition:** A minor arc is an arc of a circle that is smaller than a semicircle (les

1. **Problem Statement:** Identify which angle among \(\angle DOB\), \(\angle BAC\), \(\angle EAC\), and \(\angle ABE\) is a central angle in the given circle. 2. **Definition:** A

1. **Problem Statement:** Identify which angle among \(\angle DOB\), \(\angle BAC\), \(\angle EAC\), and \(\angle ABE\) is an inscribed angle in the given circle. 2. **Definition:*

1. The problem asks to identify which arc in the figure represents a semicircle. 2. A semicircle is an arc that represents exactly half of a circle, which means it subtends an angl

1. **Problem Statement:** We are given a circle with a chord of length 5, and a point outside the circle connected to the circle by two segments of lengths 4 and 3. We need to find