📐 geometry

1. **State the problem:** We have a right square pyramid with an altitude (height) of 10 units and a base side length of 6 units. We need to find the distance from the apex (top) t

1. **State the problem:** We need to find the image of rhombus BCDE after a 90° anticlockwise rotation around the origin. 2. **Recall the rotation formula:** For a point $(x,y)$, a

1. **State the problem:** We want to find the perimeter of a quadrilateral formed by two scalene triangles. We only know two sides of one triangle and one side of the other. 2. **U

1. **Problem 106: Find the length of X in the right triangle**. Given a right triangle with legs 4 and 4, and hypotenuse 7, find the length of segment X.

1. **Problem statement:** The areas of a circle and a rectangle are equal, and the area of the shaded region (the overlapping part) is 10 cm². We need to find the area of the recta

1. **הבעיה:** במשולש ABC חסום במעגל, נקודה N על הקשת AB היא מרכז מעגל העובר דרך A ו-B וחותך את המיתר AC בנקודה D. המיתר NC חותך את המעגל שמרכזו N בנקודה E ואת המיתר AB בנקודה F. נד

1. **Problem Statement:** Enlarge each shape by the given scale factor using the specified centre of enlargement.

1. The problem is to enlarge shapes by given scale factors from specified centres of enlargement. 2. The formula for enlargement of a point $(x,y)$ from centre $(x_c,y_c)$ with sca

1. **State the problem:** We have an isosceles triangle LMN with LM = LN. Lines AMB and CLN are parallel.

1. The problem asks to find the number of symmetry lines of a figure that is a circle divided into eight triangular sectors by radial lines. 2. A circle itself has infinite lines o

1. The problem asks to determine the shape of the cross-section formed by a horizontal plane intersecting the left and right faces of a cube. 2. A cube has six square faces, all ed

1. **Stating the problem:** We need to find the perimeter of the shaded region, which consists of an arc length plus three other segments labeled (1), (2), and (3).

1. **Problem statement:** Given a circle with center O and radius 8 m, points P, Q, and R lie on the circumference. OPQ is a straight line, \(\angle QOR = 36.9^\circ\), and OR is p

1. **Problem statement:** We need to find the length of segment $AD$ in a triangular pyramid with given angles and side lengths. 2. **Given data:**

1. **State the problem:** We are given pairs of adjacent angles on a straight line. Adjacent angles on a straight line are supplementary, meaning their sum is 180°. 2. **Formula us

1. The problem asks to visualize the 3D shape formed by two concentric squares positioned vertically with lines connecting them, enclosed in a larger rectangle, and considering the

1. The problem asks to identify the 3D shape represented by the nested squares and labeled points in the diagram. 2. The diagram shows two nested squares, one above the other, conn

1. The problem asks to visualize a 3D shape based on a description of two large squares stacked vertically, each containing a smaller square inside, connected by four parallel vert

1. The problem is to find the area, but the shape or figure is not specified. 2. To find the area, we need to know the type of figure (e.g., rectangle, triangle, circle) and its di

1. **Stating the problem:** We have a parallelogram ABCD with sides AB = 21 cm, BC = 25 cm, and angle BAD = 57°.

1. The problem is to understand and apply formulas in analytic geometry. 2. Analytic geometry uses coordinates and algebra to study geometric problems.