📐 geometry

1. The problem is to find the area of a rectangle. 2. The formula for the area of a rectangle is $$\text{Area} = \text{length} \times \text{width}$$.

1. **State the problem:** We are given that the angles in a triangle are in the ratio $1 : 2 : 9$ and we need to find the size of the largest angle. 2. **Recall the rule:** The sum

1. **State the problem:** We need to find the perimeter and area of triangle $CDE$ with vertices $C(4, -1)$, $D(4, -5)$, and $E(2, -3)$. 2. **Find the lengths of the sides for the

1. **State the problem:** We need to classify the pairs of angles $\angle x$ and $\angle y$, and $\angle y$ and $\angle z$ from the given diagrams.

1. **State the problem:** We need to reflect a quadrilateral with vertices at $ (4, -2), (6, -5), (8, -6), (9, -5) $ over the horizontal line $ y = -1 $. 2. **Formula for reflectio

1. **State the problem:** We need to reflect a triangle with vertices at $ (1, -2)$, $ (4, -3)$, and $ (1, -8)$ across the vertical line $x = -1$. 2. **Reflection formula:** When r

1. **State the problem:** We need to prove that for a right triangle $\triangle ABC$, the identity $(\sin (A))^2 + (\cos (A))^2 = 1$ holds. 2. **Recall definitions:**

1. **State the problem:** We need to complete two geometry postulates involving intersections and points.

1. **State the problem:** We have a shape formed by joining a hemisphere and a cone. The total surface area of this shape is $33\pi$ cm$^2$. The radius of the hemisphere (and cone

1. **State the problem:** We have a composite solid made of a cylinder joined to a hemisphere. The total surface area is given as $$176\pi$$ m². We need to find the radius $$r$$ of

1. **State the problem:** We have a shape made by joining a cone to a hemisphere. The total surface area of this shape is $156\pi$ cm². The radius of the hemisphere (and the base o

1. **State the problem:** We have a solid cylinder of height $11$ m and radius $4$ m. A cone with the same base radius $4$ m and slant height $9$ m is removed from the top of the c

1. **State the problem:** We need to find the surface area of a gas tank shaped as a cylinder with a hemisphere on each end. The cylinder diameter is $35$ cm, and the total length

1. **State the problem:** We are given three rays $SD$, $SE$, and $SG$ with $SE$ between $SD$ and $SG$. The measures of angles are:

1. **Stating the problem:** We need to determine the relationship between two adjacent angles when their exterior sides are perpendicular. 2. **Understanding the problem:** Adjacen

1. The problem appears to involve coordinates and labels for points or locations: "top-left: Corky Co 190", "top-right: 14.5 207.2", "center: Dingo Inc 190", "center-right: 14.5 20

1. **State the problem:** We need to find the area of a regular hexagon with side length $6$ inches. 2. **Formula for the area of a regular hexagon:** The area $A$ of a regular hex

1. **State the problem:** We are given the formula for the circumference of a circle, which is $A = 2\pi r$.

1. **State the problem:** We are given the equation of a circle $$(x-5)^2 + y^2 = 49$$ and need to find its area in square units. 2. **Recall the formula for the area of a circle:*

1. **State the problem:** Find the lengths of segments on a number line and solve for variable $x$ in a segment addition problem. 2. **Given points on the number line:**

1. **State the problem:** Find the distance between points $J(-3,4)$ and $K(2,-4)$. 2. **Formula:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: