📐 geometry

1. **Stating the problem:** We have a trapezoid ABCD with base AB as the diameter of a semicircle centered at point S. The trapezoid has height $v=6$ cm, the top side DC measures 4

1. Let's clarify the problem: we need to find angle $c$ in a triangle or geometric figure. 2. To find angle $c$, we need more information such as the other angles or sides of the t

1. **Stating the problem:** We have a parallelogram ABCD with sides |AB| = 5 cm, |BC| = 5.5 cm, and angle BAC = 45°. 2. **Understanding the figure:** In parallelogram ABCD, diagona

1. The problem asks for the formula of the area of a semicircle in terms of radians. 2. A semicircle is half of a full circle.

1. **State the problem:** We are given a triangle with vertices A, B, and C. Side AB = 10 cm, side AC = 8 cm, and angle B = 40°. 2. **Identify what is asked:** Find the size of ang

1. **State the problem:** We are given a triangle with angles $\angle EBH = 47^\circ$, $\angle ABE = 36^\circ$, and side length $BH = 7$ cm. We need to find the length of $AE$ to 2

1. **State the problem:** We are given a cuboid with angles $\angle EBH = 47^\circ$ and $\angle ABE = 36^\circ$, and length $BH = 7$ cm. We need to find the length $AE$ to 2 decima

1. **State the problem:** We have two similar cones. The smaller cone has volume $704$ mm³ and radius $8$ mm. The larger cone has volume $19,008$ mm³ and radius $r$. We need to fin

1. **State the problem:** We have a circle $C$ with equation $$x^2 + y^2 - 2x + 6y - 30 = 0.$$ Points $P(3,3)$ and $Q(7,-5)$ lie on $C$. We need to:

1. **State the problem:** We have two shapes, C and D, each with an area of $3^2 \times 13^2$ cm$^2$.

1. The problem asks to identify the types of angles marked in three different diagrams involving parallel lines and a transversal. 2. For (a), the two green angles are on opposite

1. Problem 22: Identify the terms related to a circle. - a. Tangent: A line that touches the circle at exactly one point.

**Problem 1:** Amy runs around a circular track. 1. a) Find the circumference if 8 laps equal 2000m.

1. **State the problem:** Calculate the volume of each given 3D shape using the provided dimensions. 2. **Cylinder (a):** Diameter = 80 cm, Height = 150 cm.

1. **State the problem:** We have a right triangle ABC with a right angle at B. The side BC opposite the 34° angle at C has length 3. We need to find the hypotenuse AB. 2. **Identi

1. **State the problem:** We have a right triangle with vertices I, J, and H. The right angle is at vertex I. The angle at vertex J is 54° and the side JH (hypotenuse) has length $

1. **Énoncé du problème :** Nous avons un triangle ABC avec Q milieu de [AC] et P un point sur la droite (BC) tel que BP = BC.

1. **State the problem:** We need to find the vector that translates shape J to shape L and determine if this vector can be found without using the grid.

1. **Stating the problem:** We have a right-angled trapezoidal prism with bases 4 cm and 3 cm, height 12 cm, and volume 456 cm³. We need to calculate the surface area correct to 1

1. **State the problem:** We need to find the equation of the line of reflection that maps shape F to shape G. 2. **Analyze the positions:** Shape F is around coordinates $(7,7)$ t

1. The problem states that the shape is reflected in the y-axis. 2. Reflection in the y-axis changes the x-coordinate of any point from $x$ to $-x$, while the y-coordinate remains