📐 geometry

1. **Problem:** Calculate the length |BE| to 1 decimal place. 2. **Given:** From the diagram, segment EC = 10.67 m, EF = 5.4 m, FC = 9.2 m, and BC = 3.1 m.

1. **State the problem:** Calculate the area of a square with side length 8 cm. 2. **Formula:** The area $A$ of a square is given by the formula:

1. **State the problem:** Calculate the area of a rectangle with length 9 cm and width 3 cm. 2. **Formula:** The area $A$ of a rectangle is given by the formula:

1. **State the problem:** We have a right triangle PQR with a right angle at P. 2. **Given:** Side PR = 52 cm, side PQ = 57.6 cm.

1. **Stating the problem:** We have a right triangle QRS with a right angle at Q. 2. **Given data:** Side QS = 2.25 cm and side QR = 3 cm.

1. **Problem statement:** Ju Shen designs a plastic cover shaped as a cylinder with a hemisphere on top, open at the bottom. The cylinder has height $h$ cm and radius $r$ cm. 2. **

1. **Problem statement:** Kailash manufactures a cuboid container with a square base of side length $l$ cm and height $d$ cm, where $d$ is three times $l$. The container holds 375

1. **State the problem:** Kailash manufactures a cuboid container with a square base of side length $l$ cm and height $d$ cm, where $d$ is three times $l$. The container holds 375

1. **State the problem:** We have a triangle sharing a side with an irregular pentagon. We need to find the size of angle $p$ in the triangle. 2. **Identify given angles:** The pen

1. **Problem statement:** Calculate the perimeter and area of the triangle with sides 12.2 cm, 12.2 cm, and base 14 cm, and height 10 cm. 2. **Formulas:**

1. The problem involves finding the coordinates of the vertices K', L', M', and N' of a quadrilateral or trapezoid-like polygon after a transformation. 2. To solve this, we need to

1. **State the problem:** We have a point $P(6, -7)$ and its image after reflection $P'(6, 7)$. We need to determine over which axis the point was reflected. 2. **Recall reflection

1. **State the problem:** We need to plot and label points A, B, C, and D given in polar coordinates on a polar coordinate grid. 2. **Recall polar coordinates:** A point in polar c

1. **State the problem:** We need to find the volume of a cylindrical grain silo with diameter 14 ft and height 38 ft. 2. **Formula for volume of a cylinder:**

1. **State the problem:** We need to find the volume of a cylindrical water tank with radius $r=5.5$ ft and height $h=16$ ft. 2. **Formula for volume of a cylinder:**

1. **State the problem:** We are given a circle with center O and points A, B, C, D, and E on the circle. We need to find the measures of angles and arcs: m\angle A, mCE, m\angle C

1. **State the problem:** We are given a circle with center O and points A, B, C, D, E on the circle. We need to find the measures of angles and arcs: m\angle A, mCE, m\angle C, m\

1. **State the problem:** Find the magnitude (length) of the vector or segment $\overrightarrow{AB}$ using the Pythagorean theorem. 2. **Formula:** The Pythagorean theorem states t

1. **Nêu bài toán:** Chứng minh tam giác DAC cân tại điểm C. 2. **Phân tích hình:** Tam giác DAC có các điểm D, A, C. Để chứng minh tam giác DAC cân tại C, ta cần chứng minh hai cạ

1. **Stating the problem:** We are given a figure with several intersecting lines and angles labeled as 80°, w°, 64°, x°, y°, z°, and 51°. We need to find the values of the unknown

1. **Stating the problem:** We have a figure with two pairs of parallel lines intersected by a diagonal line, creating several angles labeled $z^\circ$, $y^\circ$, $44^\circ$, $x^\