📐 geometry

1. **State the problem:** We have a square pizza box with an 8-slice circular pizza inside. The box's side length is 5 cm longer than the pizza's diameter. The area of the box's to

1. **State the problem:** Classify the given triangle by its sides and angles. 2. **Analyze the triangle:** The triangle has a right angle (indicated by the right-angle marker) and

1. **State the problem:** Find the volume of a rectangular prism with length $9$ cm, width $6$ cm, and height $4.5$ cm. 2. **Formula:** The volume $V$ of a rectangular prism is giv

1. **State the problem:** Find the volume of a rectangular prism with dimensions 6 cm, 9 cm, and 4.5 cm. 2. **Formula:** The volume $V$ of a rectangular prism is given by the produ

1. **State the problem:** We have a rectangular prism with a square base, volume $3600$ m³, and height $20$ m. We need to find the length of one side of the square base. 2. **Formu

1. **Problem:** Find the distance between points C(-2, 2) and D(4, -1) on a coordinate plane where each unit equals 25 miles. 2. **Formula:** Use the distance formula derived from

1. **Problem Statement:** Find the length of the diagonal of a basketball court that is 94 feet long and 50 feet wide. 2. **Formula:** Use the Pythagorean Theorem: $$a^2 + b^2 = c^

1. **Problem Statement:** Given right triangle $\triangle RST$ with right angle at $S$, and sides $RS = ST$. The hypotenuse $RT$ is 18 inches. Find the area of $\triangle RST$.

1. **Stating the problem:** We need to identify the types of angles present in each of the given quadrilaterals based on the descriptions: obtuse angles only, acute angles only, ac

1. **State the problem:** We have a rectangle with vertices A(-3, -3), B(1, -3), C(1, -5), and D(-3, -5).

1. **State the problem:** We have a rectangle with vertices A(-3, -3), B(1, -3), C(1, -5), and D(-3, -5). We need to find the coordinates of the image after rotating the rectangle

1. **State the problem:** We are given a parallelogram ABCD with angles labeled as follows: \(\angle D = (x+8)^\circ\), \(\angle A = (y+9)^\circ\), and \(\angle C = (3x)^\circ\). W

1. **State the problem:** We are given a rectangle with angles labeled as $(9x - 6)^\circ$ and $(2x + 8)^\circ$ at certain vertices, and we need to solve for $x$. 2. **Recall prope

1. **State the problem:** We are given a kite-shaped quadrilateral with two angles labeled as $(5x - 1)^\circ$ and $8x^\circ$. We need to find the value of $x$. 2. **Recall kite pr

1. **State the problem:** We have a rectangle ABCD with diagonals AC and BD. The lengths of the diagonals are given as expressions: AC = $9x + 20$ and BD = $10x + 8$. 2. **Importan

1. **State the problem:** We need to find the measure of angle $\angle 3$ in a kite-shaped quadrilateral where one angle is given as $27^\circ$.\n\n2. **Recall kite properties:** I

1. **State the problem:** We have parallelogram RSTU with sides labeled as follows: - Top side RS = $2a$

1. **State the problem:** We have a right triangle with sides labeled 5, 6, $y-1$, $x-2$, and 10, and we want to find the unknown values $x$ and $y$ using proportions. 2. **Set up

1. **State the problem:** Find the area of the irregular polygon with given side lengths 10 cm, 7 cm, 2 cm, 2 cm, 3 cm, and 10 cm. 2. **Analyze the shape:** The figure can be decom

1. The problem asks to identify which two angles are adjacent in a four-ray angle diagram with angles labeled 1, 2, 3, and 4 around a common vertex. 2. Adjacent angles share a comm

1. **Stating the problem:** We need to determine which two angles are adjacent from the given options. 2. **Definition of adjacent angles:** Adjacent angles share a common vertex a