📐 geometry

1. **Stating the problem:** We are given four diagrams (a, b, c, d) described as nets and asked to determine which are nets, identify the 3D objects they form, verify the answers,

1. **State the problem:** We have quadrilateral ABCD with given angles $m\angle B = 65^\circ$, $m\angle D = 48^\circ$, and sides $CD = 15$, $AD = 21$, $AB = 17$. Points B, C, and D

1. **State the problem:** We need to find the perimeter of the quadrilateral with vertices D, B, A, and C. 2. **Identify the given lengths:**

1. **Stating the problem:** We have a polygonal chain with vertical segments labeled $e$, $a$, and $b$. We want to find a relationship or solve for one of these variables based on

1. **Problem:** Find the volume of a cylinder with diameter 18 cm and height 38 cm. Round to the nearest tenth. 2. **Formula:** Volume of a cylinder is given by $$V = \pi r^2 h$$ w

1. **State the problem:** We have a right triangle ABC with a right angle at B. Side AC (the hypotenuse) is 6 units long, and angle A is 29°. We need to find the length of side opp

1. **State the problem:** We have a right triangle ABC with a right angle at A. The hypotenuse BC is 29 units, angle C is 35 degrees, and we need to find side AB labeled as $x$. 2.

1. **State the problem:** We have a right triangle with angle $A = 39^\circ$, right angle at $B$, and side $BC = 2$. We need to find side $AC = x$. 2. **Identify the sides relative

1. **State the problem:** We need to find the missing width $w$ of a rectangular prism given its volume and two other dimensions. 2. **Given:**

1. **State the problem:** We need to find the missing height $h$ of a rectangular prism given its volume and base dimensions. 2. **Formula:** The volume $V$ of a rectangular prism

1. **Stating the problem:** We have a right triangle with two sides of length 5 m each and an angle of 30° between them. We want to find the length of the third side or verify the

1. **State the problem:** Given a right triangle with points J, L, K, and point M on segment JK, with JM = 4 and JK = 9, find the length LK. 2. **Understand the setup:** Since M li

1. **Problem statement:** We want to find the value of the angle $x$ given that triangle PQR is divided into two isosceles triangles PQS and SQR, with angles at P and Q in these tr

1. **Problem statement:** We have a large triangle PQR with point S on segment PR, forming two smaller isosceles triangles PQS and SQR. The angle at vertex P in triangle PQR is $x^

1. **State the problem:** We are given a triangle \(\Delta XYZ\) with side lengths \(x = 850\) cm, \(y = 460\) cm, and \(z = 590\) cm. We need to find the area of this triangle to

1. **State the problem:** We are given triangle $\triangle STU$ with side $t = 2.7$ inches, angle $\angle T = 81^\circ$, and angle $\angle U = 72^\circ$. We need to find the area o

1. **State the problem:** We need to find the area of a trapezoid with parallel sides of lengths 4 cm and 7 cm, and a height of 4 cm. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We are given two angles, $y$ and $68^\circ$, that are adjacent and together form a right angle (which is $90^\circ$). 2. **Formula used:** The sum of angl

1. **Stating the problem:** We are given angles labeled as $h = 93^\circ$, $m = 122^\circ$, and need to find the values of $g$ and $k$ based on the given diagram and angle relation

1. **Stating the problem:** We have four angles formed by two intersecting lines: angles $h$, $g$, $m$, and $k$. Given are $h = 93^\circ$ and $m = 122^\circ$. We need to find the v

1. **Stating the problem:** We have a circular sector with radius $r=25$ meters and central angle $\theta=20^\circ$. The length $L=8.7$ meters and perimeter $P=58.7$ meters are giv