📐 geometry

1. **Problem statement:** We have a hollow shape made from four right-angled triangular tiles and four square tiles. Each triangular tile has sides 3 cm and 4 cm, and the shape is

1. **Problem Statement:** Construct a line segment AB of length 7.5 cm, its perpendicular bisector, a semicircle with AB as diameter, and perform several geometric constructions in

1. **Problem Statement:** We have several problems involving volumes and areas of prisms, cylinders, and tanks.

1. **Problem statement:** We need to find the area of the shaded minor segment in a quadrant of a circle with radius 6 cm. 2. **Understanding the problem:** A quadrant is one-fourt

1. **Problem statement:** We have a circle with radius $r=3$ cm and a minor sector with central angle $\theta=135^\circ$. We need to find the area of the minor segment and the peri

1. **Problem statement:** We have an equilateral triangle ABC with side length 10 cm. A circle centered at point A intersects the midpoints of sides AB and AC. We need to find the

1. **Problem statement:** We have a fan with radius $30$ cm and $4$ blades, each blade subtending a central angle of $30^\circ$. We need to find the total area covered by the $4$ b

1. **State the problem:** We have a circular cake with radius $r=10$ cm. We want to cut it into identical sector pieces, each with a perimeter of approximately 23.93 cm.

1. Énoncé du problème : ABCD est un parallélogramme avec les longueurs suivantes : $DA=6$, $DB=9$, $DE=2$, et $AB=8$. 2. Rappel : Dans un parallélogramme, les côtés opposés sont ég

1. **Problem statement:** We need to find the volume of the triangular prism given angle $\angle BDE = 25^\circ$, length $BD = 63$ m, and base length $AD = 21$ m. 2. **Understandin

1. **Problem Statement:** We need to find ten times the perimeter of the shaded semicircle with diameter 10 cm. 2. **Formula for the perimeter of a semicircle:** The perimeter $P$

1. **Problem statement:** Prove that triangle OAS is isosceles with principal vertex A.

1. **Problem Statement:** We have an isosceles triangle inscribed in a circle with two equal sides meeting at the top vertex called the "centre." The angles at the base are labeled

1. **State the problem:** We are given two triangles ABC and ECD with AB parallel to ED, and lines ACD and BCE are straight. We know the lengths AB = 8 cm, AC = 4.8 cm, BC = 6.4 cm

1. **Problem statement:** A cone is divided into a small cone and a frustum. The curved surface area of the small cone is $15\pi$ cm², the curved surface area of the frustum is $12

1. **State the problem:** We have a circle with equation $$(x - 5)^2 + y^2 = 25$$ and a point $$P(8,4)$$ on the circle. We need to find the y-coordinate of point $$Q$$ where the ta

1. **Problem Statement:** We have a quadrant ABC which is a quarter circle with center A and radius AB = 12 cm.

1. **Problem Statement:** Two chords AB and CD intersect at right angles at point P inside a circle. Given lengths are AP = 4, PB = 12, CP = 8, and PD = 6 units. We need to find th

1. **Problem Statement:** Mahati draws a kolam pattern on a 3x3 grid of dots spaced 1 unit apart horizontally and vertically. The continuous line encloses all dots, crossing itself

1. **Problem Statement:** We are given four side lengths: 5, 9, 12, and 13, and asked to solve the triangle. However, a triangle can only have three sides. We need to clarify which

1. **Problem Statement:** We have a right triangle with angles 30°, 60°, and 90°. The hypotenuse is 9 meters, the side opposite the 30° angle is 9 meters, and the side adjacent to