📐 geometry

1. The problem is to draw two triangles connected by vertical projection lines with given measurements: $\Delta x = 60$ mm, $\Delta y = 65$ mm, $\Delta z = 40$ mm, and $\psi = 30^\

1. The problem states that the volume of a cube is 125 cm\(^3\). We need to find its total surface area. 2. Recall the formulas:

1. **State the problem:** We are given a prism with a cross-sectional perimeter of 36 cm and a cross-sectional area of 54 cm². The length of the prism is 15 cm. We need to find the

1. **State the problem:** We are given a prism with a lateral surface area of 175 cm² and a cross-sectional area of 40 cm². We need to find the total surface area of the prism. 2.

1. The problem states that the lateral surface area and the cross-sectional area of a prism are both 175 cm². 2. The lateral surface area (LSA) of a prism is the perimeter of the b

1. **State the problem:** We are given a prism with a cross-sectional perimeter of 48 cm and a length of 10 cm. We need to find the lateral surface area of the prism. 2. **Recall t

1. **State the problem:** We have a scalene triangle ABC with sides BC = 85.94, AC = 74, and an angle of 45 degrees at vertex B. We want to find the length of side AB and the heigh

1. **State the problem:** We need to find the length of the diagonal $AG$ in the cuboid, given angles $27^\circ$ and $42^\circ$ at vertex $A$, and the base edge $AD = 63$ mm. 2. **

1. **State the problem:** We need to find the length of the edge $AG$ in the cuboid, given angles $27^\circ$ and $42^\circ$ at vertex $A$, and the length $AD = 63$ mm. 2. **Analyze

1. **Problem Statement:** Given two isosceles triangles $\triangle ABC$ and $\triangle DBC$ on the same base $BC$, with vertices $A$ and $D$ on the same side of $BC$, and $AD$ exte

1. **State the problem:** Calculate the area of a quadrilateral with sides $AB=708$, $BC=584$, $CD=706$, $DA=609$, and diagonals $AC=915$, $BD=931$. 2. **Approach:** We can split t

1. The problem asks for the total surface area of two garage doors. 2. The left door has a width of $2.5$ m and a height of $2$ m.

1. **Problem Statement:** Construct quadrilateral ABCD with given sides and diagonals: AB = 6.8 cm, AD = 5.8 cm, AC = 8.9 cm, BD = 7.3 cm, BC = 4.1 cm. 2. **Step 1: Draw diagonal A

1. **Find the length of the segment indicated in the top-left circle with two secants:** Given: Outside segments 6 and 8, inner segment unknown (call it $x$).

1. **State the problem:** We have a frustum formed by removing a smaller cone from a larger cone. The larger cone has height 45 cm, the smaller cone removed has height 9 cm and bas

1. The term "scale factor" typically refers to the ratio by which a figure is enlarged or reduced in size in geometry. 2. It is the multiplier used to increase or decrease the dime

1. **Problem 1:** If arcs APB and CQD of a circle are congruent, find the ratio of AB : CD. Since arcs APB and CQD are congruent, their corresponding chords AB and CD are equal in

1. The problem asks to identify features that all squares have but some rhombuses do not. 2. A square is a special type of rhombus where all sides are equal and all angles are righ

1. The problem asks for the size of angle $a$ in the triangle formed by points $A$, $B$, and $C$ on the circle. 2. Since points $A$, $B$, and $C$ lie on a circle, the triangle $ABC

1. **State the problem:** We are given a triangle with angles 70° and 61°, and the side opposite the 61° angle is 15 units. We need to find the length of the side opposite the 70°

1. **State the problem:** Given that $\angle SUT \cong \angle YXZ$, prove that the vectors $\overrightarrow{WY}$ and $\overrightarrow{TV}$ are parallel. 2. **Analyze the given info