📐 geometry

1. The problem states that $DF = DE + EF = 11 + 4 = 15$ meters, but the length is given as 11.7 meters without using the hypotenuse formula. 2. This suggests that $DF$ is the sum o

1. **State the problem:** We have a polygon ABCDEF with given conditions: BCD is a straight line, CA is parallel to DF, angles ABD, BDE, and DEF are right angles, and lengths AB =

1. **State the problem:** We need to find the translation that maps Figure T onto Figure U. 2. **Identify coordinates:**

1. **State the problem:** We have a prism with two regular hexagonal faces, each with an area of 23 cm². The height (length) of the prism is 8 cm, and the edge length of the hexago

1. **Problem Statement:** We have a prism with a regular decagonal cross-section. Each side of the decagon is 2 cm, and the height of the prism is 14 cm.

1. **State the problem:** We need to find the surface area of a triangular prism with given dimensions. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 7 m, 4 m, and 3 m, and the prism length (height) is 11 m. 2. **

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base having sides 7 m, 9 m, and a height of 3 m to the base 7 m, and the prism le

1. **State the problem:** We need to find the surface area of a triangular prism with a right triangle base where the legs are 7 m and 4 m, the hypotenuse is 9 m, and the prism hei

1. **State the problem:** We need to find the surface area of a triangular prism with a triangular base of base $8$ cm and height $15$ cm, a slant edge of $17$ cm, and prism length

1. **Problem Statement:** We have a right prism with an equilateral triangle base of side length 7 cm and a prism height (length) of 8 cm.

1. **Problem statement:** We have a prism with an equilateral triangular cross-section. The base of the triangle is 7 cm, and the prism's length (depth) is 8 cm.

1. **Problem statement:** We have a triangular prism with an equilateral triangle cross-section where each side of the triangle is 7 cm, and the length of the prism is 8 cm.

1. **State the problem:** We need to find the value of angle $x$ in quadrilateral $ABCD$ composed of two triangles $ABC$ and $BCD$ with given sides and angles. 2. **Given data:**

1. **State the problem:** We are given a right-angled triangle AOC with AC = 24 cm, OC = 26 cm, and angle \(\angle AOC = 60^\circ\). Inside it is a children's swimming pool shaped

1. **Problem statement:** We have an equilateral triangle formed by towns L, M, and N. The bearing of M from L is 103°. We need to find the bearing of L from N. 2. **Understanding

1. **Problem statement:** Prove using vectors that the diagonals of a rhombus bisect each other. 2. **Setup:** Let the rhombus have vertices represented by vectors \( \vec{A}, \vec

1. Stating the problem. A wall 10 m long, 20 cm thick and 1.2 m high is constructed as a partition between two plots of land.

1. **State the problem:** We have a wall with dimensions length = 10 m, thickness = 20 cm = 0.2 m, and height = 1.2 m. We need to find the cost of cementing five sides of this wall

1. **State the problem:** We need to find the area of an L-shaped polygon composed of two rectangles and a triangular cutout. 2. **Identify the shapes and dimensions:**

1. The problem is to explain the mensuration formulas for a cylinder and a sphere. 2. For a cylinder, the important measurements are its radius $r$ and height $h$.