📐 geometry

1. **State the problem:** We need to find the area of a square field given that its perimeter is 20 cm. 2. **Recall the formulas:**

1. **Stating the problem:** We are given a triangle with two equal sides and an included angle of 25° between them. We need to find the measures of angles 1 and 2. 2. **Important r

1. **State the problem:** Find the area of a trapezoid with top base $19$ m, bottom base $30$ m, and height $6$ m. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We are given two points in polar coordinates, $P_1 = (-3, \frac{5\pi}{6})$ and $P_2 = (4, \frac{4\pi}{3})$, and we need to find the area of the triangle f

1. Problem 5: Given the equation $a^2 + b^2 = c^2$ with $16^2 + x^2 = 25^2$, find $x$. 2. Use the Pythagorean theorem formula:

1. **State the problem:** Find the value of $x$ in the right triangle where the sides satisfy the Pythagorean theorem. 2. **Formula:** The Pythagorean theorem states that for a rig

1. Problem 5: Given a circle with center P, diameters FH and EG intersecting at P, and the angle between EP and GP is 38°, find the measure of arc DGE. 2. Since FH and EG are diame

1. **Problem:** PQRS is an isosceles trapezoid with median MD. Given $SM = 4x + 5$ and $MP = 7x - 10$, find $RD$ and $DQ$. 2. **Formula and rules:** In an isosceles trapezoid, the

1. **Problem statement:** We have a right triangle with legs of lengths 2 units and 4 units. We want to find the area of the square that shares its side with the hypotenuse (the th

1. **State the problem:** Desiree needs to find the total area to cover with stone pavers, which includes the patio and the walkway.

1. **Problem 5: Find the circumference and area of the circle with radius $\sqrt{2}$ cm.** 2. The formulas for circumference and area of a circle are:

1. **Stating the problem:** We have a quadrilateral inscribed in a circle with two known angles 70° and 80°, and two unknown angles labeled $\alpha$ and $\beta$. We need to find th

1. **Énoncé du problème :** Calculer les mesures des angles $\alpha$, $\beta$ et $\gamma$ dans un triangle inscrit dans un cercle de centre $O$, sachant que l'angle central $\angle

1. The problem asks us to determine side lengths that satisfy the triangle inequality theorem. 2. The triangle inequality theorem states that for any triangle with sides $a$, $b$,

1. **State the problem:** We need to find the value of angle $x$ in a triangle where two exterior angles are given: $120^\circ$ at vertex A and $112^\circ$ at vertex C. 2. **Recall

1. **Problem A: Find the measure of each arc of circle ⊙P.** Given: Circle with center P, points A, B, C on circumference. Angle at center P between radii PC and PB is 57°.

1. **State the problem:** We need to find the height of the flagpole, which is the vertical leg of a right triangle. 2. **Identify the known sides:** The horizontal leg is 10 ft, t

1. **State the problem:** We are given a triangle ABC with segment DE inside it, where AB = $11x - 25$ and DE = $4x + 1$. We need to find the length of DE. 2. **Identify the relati

1. **Problem Statement:** We have three lines intersecting at point H: MK, HJ, and HL. Given angles are:

1. **State the problem:** We need to find the distance traveled by a tire after 3 full rotations. The tire has a diameter of 28 inches. 2. **Formula used:** The distance traveled i

1. **Problem statement:** Prove that in an equilateral triangle ABC with points D, E, F on the perpendiculars from an arbitrary point P to the sides, the equality $BD + CE + AF = D