📐 geometry

1. **Problem statement:** We have two circles: a smaller circle with center A and radius $r$ passing through points B, C, and D, and a larger circle with center C and radius $s$ pa

1. დავწეროთ მოცემული პირობა: ორი მსგავსი სამკუთხედის პერიმეტრები შეეფარდება როგორც $10:9$. 2. პირველი სამკუთხედის გვერდების შეფარდება არის $6:7:8$.

1. **Problem Statement:** Find the midpoint of a line segment given endpoints, and find the other endpoint given one endpoint and the midpoint.

1. დავწეროთ მოცემული პირობა: ორი მსგავსი სამკუთხედის პერიმეტრები შეეფარდება ერთმანეთს როგორც $10:9$. 2. პირველი სამკუთხედის გვერდების შეფარდება არის $6:7:8$.

1. **Problem Statement:** Calculate the area of the shaded part formed by the intersection of the given shapes inside the square of side length 16.

1. **Problem statement:** (a) Show that $s = \sqrt{3} r$ given the two circles and points described.

1. **Problem statement:** We have two circles: one with center A and radius $r$ passing through points B, C, and D, and a larger circle with center C and radius $s$ passing through

1. **State the problem:** We have a circle with diameter endpoints P(1,1) and Q(7,11).

1. The problem asks us to find the area of the shaded part. 2. To find the area of a shaded region, we typically need to know the boundaries of the region, such as curves, lines, o

1. **Problem statement:** (a) Show that $s = \sqrt{3} r$ where $s$ is the radius of the larger circle centered at $C$ passing through $B$ and $D$, and $r$ is the radius of the smal

1. **Problem Statement:** We have a cuboid PQRSTUVW with edges:

1. **Problem Statement:** We have a cuboid PQRSTUVW with dimensions:

1. Let's state the problem: We need to find all the angles in a parallelogram. 2. Important properties of a parallelogram:

1. **State the problem:** We need to find the volume of an L-shaped prism made of 1 cm³ cubes by counting the cubes in its cross-section. 2. **Understand the shape:** The prism con

1. **State the problem:** We need to find the volume of an L-shaped prism made of centimetre cubes by counting the cubes in its cross-sections. 2. **Understand the shape:** The pri

1. **State the problem:** We need to find the mass of a metal prism with a given cross-sectional shape and length. The density of the metal is 8 grams per cm³. 2. **Understand the

1. **State the problem:** We have a cuboid carton with base dimensions 14 cm by 12 cm and height 18 cm. It is filled with water to a depth of 12 cm. When the carton is turned over

1. **State the problem:** We have a cuboid with dimensions 18 cm (height), 12 cm (depth), and 14 cm (width). We want to find the volume of the cuboid. 2. **Formula used:** The volu

1. **State the problem:** Lydia has a cuboid block with dimensions 35 cm by 40 cm by 25 cm. She melts it to make smaller cubes each with side length 4.5 cm. We need to find the max

1. **State the problem:** We need to find the depth of a cuboid-shaped basin that holds 158.175 litres of water. The basin's length is 95 cm and width is 45 cm. 2. **Formula used:*

1. **State the problem:** We need to find the length $z$ of a cube given its volume is 729 mm$^3$. 2. **Formula used:** The volume $V$ of a cube with side length $z$ is given by: