📐 geometry

1. **State the problem:** Find the area of a figure composed of a rectangle and two semicircles attached to the shorter sides of the rectangle. 2. **Given dimensions:** Length of r

1. **Problem statement:** In parallelogram PQRS, given that diagonal SQ = 26, find the length of segment ST, where T is the intersection of diagonals PR and SQ. 2. **Key property:*

1. The problem states that triangles \(\triangle CJW \cong \triangle AGS\), with \(m\angle A = 50^\circ\), \(m\angle J = 45^\circ\), and \(m\angle S = 16x + 5\). We need to find \(

1. **Problem statement:** We are given a triangle \(\triangle ABC\) with sides \(AB = 7.5x\), \(BC = 6x + 3\), and \(AC = 10x - 5\). The triangle is equilateral, meaning all sides

1. **State the problem:** We have a right triangle ABC with vertices A at the origin $(0,0)$, C on the x-axis, and B on the hypotenuse line $y = -0.5x + k$. The left leg is $y = 2x

1. **State the problem:** We have two similar triangles ABC and EBD with sides AB = 9 ft, AC = h, DE = 7 ft, and BE = 15 ft. We need to find the unknown side length $h$.

1. **State the problem:** We have a right triangle PQR with sides PQ = 20, QR = 21, and PR = 13. The height $h$ is drawn from the top vertex P perpendicular to the base QR. We need

1. **Stating the problem:** We have a sequence of figures where each figure is a large triangle subdivided into smaller triangles. The first figure has 1 small triangle, the second

1. **State the problem:** We have a right triangle where one leg is 1 millimeter longer than the shorter leg, and the hypotenuse is 2 millimeters longer than the shorter leg. We ne

1. **State the problem:** We are given a rectangle MNOL with sides labeled as follows: top side MN = 26, bottom side LO = 26, left side ML = 5a - 7, right side NO = 2a + 8, and ang

1. **Problem Statement:** Find the length AB of rhombus FGHI given the side length expressions. 2. **Recall Properties of a Rhombus:** All sides are equal in length.

1. **Problem 4:** In a right triangle, one acute angle is 9 times the other. Find each acute angle. 2. The sum of acute angles in a right triangle is 90° because the right angle is

1. **Problem statement:** We have a chessboard divided into four pieces: two right triangles and two trapezoids. Each small square has area 1 unit. We need to find the area of each

1) Problem 1: Given angles with expressions in terms of $x$ and $y$, find $y$ when $x=20$. 2) Problem 2: Given segment lengths with expressions in terms of $x$ and $y$, find $x$, $

1. **State the problem:** Find the distance $d$ between points $A(-5,5)$ and $B(5,-5)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(x_

1. **State the problem:** Find the distance $d$ between points $A=(11,-5)$ and $B=(1,7)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(

1. **State the problem:** We have a right triangle with legs measuring 10 cm and 24 cm, and we need to find the hypotenuse $x$ using Pythagoras' theorem. 2. **Formula:** Pythagoras

1. **State the problem:** Find the distance between the points $(0,0)$ and $(-6,5)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given b

1. **State the problem:** Calculate the area of a trapezium with parallel sides of lengths 7 cm and 3 cm, and a height of 6 cm. 2. **Formula for the area of a trapezium:**

1. The problem asks for the mathematical name of the 3D shape and the number of its faces. 2. The shape described is a hexagonal prism, which is a type of prism with hexagonal base

1. **Problem Statement:** Find the measures of the other angles of a parallelogram if one angle measures 78°.