📐 geometry

1. **Problem statement:** Calculate the length of segment AB in a rectangular prism where the edges from vertex A are 2 cm, 5 cm, and 9 cm long. 2. **Formula used:** To find the le

1. **State the problem:** We need to find the area of the top of a table composed of rectangles and triangles with given dimensions in inches. 2. **Identify the shapes and dimensio

1. **State the problem:** We need to find the area of a barn wall composed of a rectangle and a trapezoid on top. 2. **Identify the shapes and dimensions:**

1. **Problem statement:** Lily wants to paint her bedroom walls and ceiling. The room measures 4 m by 3.5 m by 2.5 m. There is a door (0.8 m × 2 m) and a window (0.96 m × 0.84 m) w

1. The problem asks to identify which of the given rays or segments is a chord of circle O. 2. A chord of a circle is a segment whose endpoints both lie on the circle.

1. **Problem Statement:** Calculate the surface area of the given shape with sides 6 cm, 12 cm, and 2 cm, where the triangle's hypotenuse is calculated using the Pythagorean theore

1. **Problem statement:** The perimeter of triangle $\triangle ABC$ is 29 m. The segment $\overline{AD}$ bisects angle $\angle A$. Given that $AB = 4$ m and $AC = 5$ m, find the le

1. **Problem Statement:** Calculate the surface area of the 3D shape with base 6 cm, height 12 cm, and depth 2 cm, given the net with side lengths 12, 72, 24, 6, 2, and \(\sqrt{40}

1. **State the problem:** Calculate the volume of the L-shaped prism with given dimensions. 2. **Understand the shape:** The prism is L-shaped, so we can split it into two rectangu

1. The problem asks to identify which of the given rays or segments is a chord of circle O. 2. A chord of a circle is a line segment with both endpoints on the circle.

1. **State the problem:** We are given two adjacent angles formed by a ray originating from a point on line segment AB. The angles are labeled $2y + 60$ and $y$. We need to find th

1. **State the problem:** We need to find the volume of a rectangular prism building with a smaller rectangular section cut out from the top corner. The main prism has dimensions 4

1. **State the problem:** Miguel's aquarium measures 70 cm by 50 cm by 30 cm. It is filled three quarters full of water. We need to find how many liters of water it contains.

1. **Stating the problem:** We have two triangles, DEF with sides 24, 18, and 28, and GHI with angles 45°, 58°, 60°, and one side length 70. We want to find missing sides or angles

1. **State the problem:** We have a right triangle with legs of lengths 9 and 15, and we need to find the length of the hypotenuse. 2. **Formula used:** In a right triangle, the Py

1. Problem 9: Find the perimeter of triangle \(\triangle MNP\) with sides \(MN=22\), \(MP=25\), and \(NP=x+4\). Given angles \(\angle M=55^\circ\), \(\angle N=34^\circ\). 2. Use th

1. **State the problem:** We need to find the length $x$ of the side opposite the $55^\circ$ angle in a triangle where the other two sides are $19$ m and $17$ m. 2. **Formula used:

1. **Problem statement:** We have a cube with side length 7 cm and surface area 294 cm².

1. **Stating the problem:** We have an original cube with volume $V = 7 \times 7 \times 7 = 343$ cm$^3$.

1. **State the problem:** Calculate the area of a rectangle with width 23 yards and height 12 yards. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. **State the problem:** Calculate the perimeter of a polygon with sides measuring 5 in., 3 in., 3 in., 5 in., 6 in., and 9 in. 2. **Formula:** The perimeter $P$ of a polygon is t