📐 geometry

1. **State the problem:** We have two adjacent triangles sharing a side of length 11. One triangle has sides 15 and 11 with an angle of 75° opposite the side of length 15. The othe

1. **State the problem:** We have two triangles with equal sides and given angles. We want to find the range of possible values for $x$ such that the side lengths and angles are co

1. The problem is to calculate the length of the right side of a right triangle. 2. We use the Pythagorean theorem which states that in a right triangle, the square of the hypotenu

1. The problem involves a right triangle with one angle of 45° and the base (askelmitta) length of 65 units. 2. Since one angle is 45° and the triangle is right-angled, the other n

1. **Problem statement:** We have a parallelogram with sides $a$ and $b$ and an angle $\alpha$ between them. Internal bisectors of the angle are drawn, and we need to find the area

1. **State the problem:** Given a circle with points L, X, W, and N on its circumference, and two intersecting lines crossing outside the circle at point V, where $m\angle WX = 62^

1. The problem is to find the length of the hypotenuse of a right triangle using Pythagoras' theorem or basic trigonometry. 2. Pythagoras' theorem states that in a right triangle,

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