📐 geometry

1. **State the problem:** Raymond has a piece of wrapping paper that measures 1 m by 1 m, which is 100 cm by 100 cm, so the total area of the paper is $100 \times 100 = 10000$ cm$^

1. The problem asks which shapes can be set up in a cookie shaper machine and why, and what these shapes have in common. 2. Convex polygons like the pentagon, hexagon, and octagon

1. The problem asks which shapes can be set up in a cookie shaper machine and what these shapes have in common. 2. Convex polygons like the pentagon, hexagon, and octagon can be se

1. The problem asks for the length of the side of a square. 2. To find the side length of a square, we need to know either the area or the perimeter.

1. **Problem statement:** A square piece of paper has four right isosceles triangles removed, one from each corner. The remaining shape is a rectangle ABCD with sides AB = 12 and B

1. **Énoncé du problème :** On a un angle $\angle ABC$ dont la mesure est donnée, et on trace la médiatrice du segment $[AB]$.

1. **Énoncé du problème :** On a un segment $AC$ et sa médiatrice $BD$. La médiatrice coupe $AC$ en son milieu en $B$, donc $B$ est le point milieu de $AC$.

1. The problem states that a polygon with vertices V(-5,7), U(3,5), T(1,-4), and S(-6,-7) is dilated by a factor of $\frac{1}{4}$ centered at the origin. 2. The formula for dilatio

1. **Problem Statement:** Find the values of angles $a$ and $b$ in the circle diagrams numbered 7 and 8.

1. **Problem Statement:** Given a circle with center O, points A, B, C, and D on the circle such that AOD \perp CB, \angle CAB = 60^\circ, AD bisects \angle CAB, and AC = 10 cm. Fi

1. **State the problem:** We need to find the surface area of a square-based pyramid with four identical triangular faces. The base side length is 30 mm, and each triangular face h

1. **State the problem:** We need to find the surface area of a square-based pyramid with a base side length of 9 cm and four identical triangular faces, each with a height of 14 c

1. **Stating the problem:** We are given two parallel horizontal lines intersected by two transversal lines, creating pairs of angles labeled a, b, c, d on the bottom intersection

1. **Problem statement:** We have a circle with points A, B, C, D on the circumference.

1. **Problem statement:** We have three parallel lines cut by a transversal, with angles labeled as in the diagram.

1. **State the problem:** Find the exact area swept by a windshield wiper of length $1.5$ m moving through an angle of $75^\circ$. 2. **Formula for area of a sector:** The area $A$

1. **State the problem:** We need to find the area swept by a windshield wiper of length $l=1.5$ m that moves through an angle of $75^\circ$. 2. **Formula for area of a sector:** T

1. **State the problem:** We have two similar trapezoidal shapes A and B. Shape A has sides: top = 4 cm, height = 12 cm, bottom = 7 cm.

1. **Stating the problem:** We have a quadrilateral with sides labeled as follows:

1. **Calculate the area of the rectangle with midpoints M(9,11) and N(5,8):** Given M and N are midpoints of two sides of the rectangle, and the sides are parallel to the axes.

1. **State the problem:** We need to find the coordinates of the center, $C$, of a rectangle given its bottom-left corner at $(4, -3)$ and top-right corner at $(18, 11)$. 2. **Form