📐 geometry

1. The problem states that quadrilateral PQRS is dilated by a scale factor of 2 with the center of dilation at the origin. We need to find the coordinates of point S' after dilatio

1. **State the problem:** We are given a quadrilateral with vertices labeled \(\pi\), \(x\), \(y\), and \(z\). The angles at vertices \(x\) and \(y\) are given as \((13x - 7)^\circ

1. **State the problem:** Calculate the distance from the center of a circle to its border given a radius. 2. **Formula:** The distance from the center to the border of a circle is

1. **State the problem:** We want to find the distance from the center of a circle to its border. 2. **Formula and explanation:** The distance from the center of a circle to any po

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 8 cm and 12 cm, and a height of 4 cm. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 8 cm and 12 cm, and a height of 4 cm. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We need to find the total surface area of a cube with edge length 3 cm. 2. **Formula:** The total surface area $A$ of a cube with edge length $s$ is given

1. **State the problem:** We need to find the total surface area of a cube with an edge length of 3 cm. 2. **Formula:** The total surface area $A$ of a cube with edge length $s$ is

1. **State the problem:** We have a rectangle with length 16 m and width 12 m. We need to shade 30% of its area on the left side and label all side lengths and right angles. 2. **C

1. **State the problem:** We have a rectangle with length 16 m and width 12 m. We need to shade 30% of its area on the left side and label all side lengths and right angles. 2. **C

1. **State the problem:** We need to find the area of a parallelogram with a base of 9 cm and a height of 5 cm. 2. **Formula for the area of a parallelogram:**

1. **State the problem:** We need to find the area of a triangle with a base of 10 cm and a height of 6 cm. 2. **Formula for the area of a triangle:**

1. **State the problem:** We need to find the area of a rectangle with length 12 cm and width 5 cm. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. **Problem statement:** We have a polygon divided into two parallelograms with given angles 48° and 117° at the top parts. We need to find the angle measure at the bottom point.

1. **State the problem:** We need to show that the quadrilateral PATR with vertices \(P(-3,3)\), \(A(3,2)\), \(T(-4,-3)\), and \(R(2,-4)\) is a parallelogram by finding the lengths

1. **State the problem:** We need to find the perimeter of a square with side length 8 cm. 2. **Formula:** The perimeter $P$ of a square is given by the formula:

1. **Problem statement:** We have a triangular dog house with sides in the ratio 2:2:1, where the shortest side (base) is 1 meter. Inside, there is a smaller triangular storage are

1. The problem asks which angles are supplementary to \(\angle 6\). Supplementary angles are two angles whose measures add up to \(180^\circ\).\n\n2. Given two intersecting lines,

1. **Problem statement:** Find the measure of angle $C$ in triangle $ABC$ with sides $AB=8$, $BC=7$, and $AC=13$. The angle to find is at vertex $C$. 2. **Formula used:** Use the L

1. **State the problem:** We need to find the measure of angle $\angle C$ in triangle $ABC$ where sides $AB=5$, $BC=10$, and $AC=11$. 2. **Formula used:** Use the Law of Cosines to

1. **Problem statement:** Find the unknown side lengths in the right triangles using the Pythagorean theorem, giving answers in surd form. 2. **Formula:** For a right triangle with