📐 geometry

1. **Problem statement:** In triangle $\triangle XYZ$, given $\angle T = 69^\circ$, side $t = 8$ cm, and side $x = 5$ cm, find the requested value (assumed to be side or angle rela

1. **State the problem:** Find the surface area of a square pyramid with a square base side length of 6 cm and slant height of 10 cm. 2. **Formula for surface area of a square pyra

1. **State the problem:** Find the surface area of a rectangular prism with dimensions 8 cm (length), 3 cm (height), and 2 cm (width) using its net. 2. **Formula for surface area o

1. **State the problem:** Find the volume of a cone with height $12$ yards and base radius $5$ yards. 2. **Formula:** The volume $V$ of a cone is given by the formula:

1. Given that \(\triangle XYZ \sim \triangle ACB\), corresponding angles are equal, so angle \(B\) in \(\triangle ACB\) corresponds to angle \(Y\) in \(\triangle XYZ\). 2. In \(\tr

1. **State the problem:** Find the volume of a sphere with radius $r=3$ cm. 2. **Formula:** The volume $V$ of a sphere is given by

1. **State the problem:** Find the volume of a triangular pyramid with base edges 3 ft and 2 ft, and height 3 ft. 2. **Formula:** The volume $V$ of a pyramid is given by

1. **State the problem:** We have trapezium ABCD with AB parallel to DC, BC perpendicular to both AB and DC, and given side lengths. We need to find the length of side AD in the fo

1. **Problem Statement:** Complete the table for a square pyramid with the number of faces (F), vertices (V), edges (E), and the sum F + V. 2. **Recall Euler's Formula for Polyhedr

1. The problem asks for the number of edges, faces, and vertices of a solid formed by folding a net of a square pyramid. 2. A square pyramid has a square base and 4 triangular face

1. The problem asks for the number of vertices and faces of a cube. 2. A cube is a three-dimensional solid object bounded by six square faces, with three meeting at each vertex.

1. **Problem Statement:** We have three parallel roads cut by a transversal road, creating several angles at intersections. We want to analyze the relationships between these angle

1. **Problem Statement:** We have three parallel roads intersected by a transversal road, creating several angles. Given that \(\angle EBC = x^\circ\), we need to find the measures

1. **State the problem:** We have a right triangle $\triangle MNO$ with $\angle O = 90^\circ$, and side lengths $NM = 85$, $MO = 84$, and $ON = 13$. We need to find the ratio that

1. **State the problem:** We have two squares, P and Q. One side of square P is 4 inches. 2. The area of square P is 4 times the area of square Q.

1. **State the problem:** We have a right triangle \(\triangle TUV\) with \(\angle V = 90^\circ\), sides \(UT = 5\), \(VU = 4\), and \(TV = 3\). We need to find \(\cos(\angle U)\)

1. **State the problem:** We have a right triangle with hypotenuse 26 cm, one leg 10 cm, and the other leg labeled $b$. We need to find the length of $b$. 2. **Formula used:** In a

1. **State the problem:** We have a right triangle with sides 9 mm, 15 mm, and an unknown side $b$. 2. **Identify the formula:** For a right triangle, the Pythagorean theorem appli

1. **State the problem:** Find the volume of a composite solid consisting of a rectangular prism with a square base of side 2 ft and height 2 ft, topped by a pyramid with a square

1. **State the problem:** We have a TV with a diagonal length of 54 inches and a width of 40 inches. We need to find the height of the TV. 2. **Formula used:** For a rectangle, the

1. **State the problem:** We need to find the volume of a cylinder with diameter 11 m and height 15 m, then convert that volume to liters and round to the nearest liter. 2. **Formu