📐 geometry

1. **State the problem:** We are given a prism with a cross-sectional area of 18 cm² and a length of 3 cm. We need to find the volume of the prism. 2. **Formula used:** The volume

1. **Stating the problem:** We have a rectangular cuboid pool with dimensions 3 m by 14 m by 9 m. We want to find the volume of the pool and then determine how many seals can live

1. **State the problem:** We have a cuboid container with dimensions length = 8 cm, width = 5 cm, and height = 10 cm. It contains 120 ml of water. Since 1 ml = 1 cm³, the volume of

1. **State the problem:** We need to find the volume of a cuboid with given dimensions. 2. **Given:**

1. **Problem statement:** We are given a cuboid with a volume of 2457 mm³. The height is 21 mm, the width is 9 mm, and we need to find the length (denoted as $l$). 2. **Formula for

1. **Problem statement:** We are given a cuboid with a volume of 3468 mm^3, height of 34 mm, width of 6 mm, and an unknown length. We need to find the length of the cuboid in milli

1. **State the problem:** We need to find the volume of water inside a cuboid container. The cuboid has dimensions width = 16 cm, depth = 7 cm, and height = 14 cm. The water level

1. **Problem Statement:** We need to find the total number of triangles of all sizes in a large triangle subdivided by vertical and horizontal lines. 2. **Understanding the Diagram

1. **State the problem:** We have a trapezoid with angles and side lengths given as follows: - Top-left angle: $90^\circ$

1. **State the problem:** We need to find the size of angle $x$ in a quadrilateral where the given angles are $105^\circ$, $72^\circ$, $218^\circ$, and $51^\circ$. The $218^\circ$

1. **State the problem:** We need to find the size of angle $x$ in an irregular quadrilateral where the other three angles are $57^\circ$, $32^\circ$, and $102^\circ$, and there is

1. **State the problem:** We are given two intersecting chords in a circle, creating two angles at the intersection point. The angles are labeled as $2x + 41^\circ$ and $12x - 19^\

1. **State the problem:** We need to find the value of $x$ given two angles in a circle: one angle is $x + 83^\circ$ and the other is $8x + 34^\circ$. 2. **Identify the relationshi

1. **State the problem:** We are given two inscribed angles in a circle, one at point U labeled $16x + 26^\circ$ and another at point R labeled $42^\circ$. We need to find the valu

1. **State the problem:** We need to find the volume of an L-shaped prism composed of two rectangular blocks. 2. **Identify dimensions:** The smaller block has dimensions 4 cm (wid

1. The problem is to find the perimeter of a shape. 2. The perimeter is the total distance around the shape, calculated by adding the lengths of all its sides.

1. **Stating the problem:** Construct triangle ABC with sides AC = 9 cm, BC = 7 cm, and angle BAC = 90°. 2. **Understanding the problem:** We have a right triangle with angle BAC =

1. **Stating the problem:** Construct triangle ABC where side AC = 9 cm, side BC = 7 cm, and angle BAC = 90°. 2. **Understanding the problem:** We have a right triangle with angle

1. The problem is to find the perimeter of a shape. 2. The perimeter of a polygon is the sum of the lengths of all its sides.

1. **Problem Statement:** Calculate the size of angle $x$ at point $A$ on the circumference of a circle with center $O$, given that angle $D$ on the circumference is $142^\circ$. 2

1. **State the problem:** We are given two vertices of a triangle, $A(2,1)$ and $B(3,-2)$, and the area of the triangle is 5. The third vertex $C$ lies on the line $y = x + 3$. We