📐 geometry

1. **State the problem:** Find the area of the right triangle with vertices A(-5, 4), B(3, 4), and C(-5, 0). 2. **Formula for the area of a triangle:**

1. Problem statement: Find the surface area of a cube with side length $a$. 2. Formula and rules: A cube has 6 congruent square faces.

1. **Problem statement:** (i) Show that the centroid of the face opposite to vertex $t$ in a tetrahedron with vertices $t, u, v, w$ is $\frac{1}{3}(u+v+w)$, and write down the cent

1. The problem is to describe a pentagon and generate its shape. 2. A pentagon is a polygon with five sides and five angles.

1. **Stating the problem:** We have a right triangle with a hypotenuse of length 15 and one leg of length 10. We need to find the area of the triangle and the length of the other l

1. **State the problem:** Find the volume and surface area of a right circular cylinder with diameter 6 inches and height 12 inches. 2. **Formulas:**

1. **Problem Statement:** We are given three locations on a coordinate plane representing a simple city map of Dubai: School at (2, 3), Mall at (2, 8), and Park at (7, 3). We need

1. **State the problem:** We have a large right triangle with a hypotenuse of 50 and a base segment of 45. Inside it, a smaller right triangle is formed by a perpendicular, with le

1. **State the problem:** We have an isosceles triangle with one side length 6.2 mm and an angle of 58° between that side and the base. We need to find the length $w$ of the base.

1. **Problem Statement:** We have a circle with center at Point A and a point B on the perimeter. We need to determine if Line AB is a radius of the circle. 2. **Definition of Radi

1. **State the problem:** We have a circle on a grid where each square measures 1 unit by 1 unit. We need to find:

1. Problem statement. I will explain what a 90 degree (right) triangle is and show a drawing.

1. The problem asks: What is a 90 degree triangle and can you show it in a drawing? 2. A 90 degree triangle, also called a right triangle, is a triangle that has one angle exactly

1. **State the problem:** Find the volume of a cone using the formula $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 2. **Formula and rules:** The vol

1. **Problem:** Find the volume of a cone with radius 4 m and height 10 m. 2. **Formula:** The volume $V$ of a cone is given by

1. **State the problem:** We have a point $P$ with coordinates $(-9, -8)$ that is dilated from the origin (center of dilation) with a scale factor of $\frac{1}{3}$. We need to find

1. **State the problem:** We need to find the size of angle ABC to the nearest degree. 2. **Understanding the setup:** The protractor is placed with the flat edge along points B to

1. The problem asks to identify the correct position of a protractor to measure the given angle accurately. 2. The correct method to measure an angle with a protractor is:

1. **State the problem:** We need to find the total surface area of a rectangular prism with dimensions given as $q$ cm (length), 4 cm (width), and 5 cm (height). Additionally, the

1. **State the problem:** Calculate the total surface area of a figure composed of a square base with side length 20 cm and four identical triangles attached to each side. Each tri

1. The problem is to find the area of a polygon. 2. The general formula for the area of a polygon depends on the type of polygon. For a simple polygon with vertices $(x_1,y_1), (x_