📐 geometry

1. The problem is to find the area of a quadrilateral. 2. A quadrilateral is a four-sided polygon. To find its area, we need more information such as the lengths of sides, height,

1. **State the problem:** Find the equation of the plane passing through the point $(1,-1,3)$ and containing the line given by $$\frac{x}{3} = \frac{y+2}{2} = \frac{z-1}{4}.$$\n\n2

1. **State the problem:** We have trapezium ABCD with BC and AD parallel, BC = 8.4 cm, AD = 17.6 cm, area = 179.4 cm², and exactly one line of symmetry. We need to find angle ABC.

1. **Problem statement:** A rectangular garden has a diagonal of 20 m and length of 16 m. A circular pond is constructed inside it.

1. **Stating the problem:** We have three polygons arranged side by side: a square, a regular hexagon, and a regular n-sided polygon. We want to understand the relationship between

1. **Nêu bài toán:** Cho tam giác ABC vuông tại A, đường cao AH. Vẽ phân giác AD của góc HAB. Tia phân giác góc B và góc C cắt nhau tại O. Chứng minh rằng $OD=OA$. 2. **Phân tích v

1. **Stating the problem:** We have a triangle \(\triangle ABC\) and we want to find the image of this triangle after an enlargement with center of enlargement at \((2,-1)\) and sc

1. **State the problem:** We have a circle with center $T$, and points $U$ and $V$ on the circle. The angle $\angle UTV$ is $50^\circ$, and the area of the shaded sector formed by

1. **Stating the problem:** We have a polygon with points C, S, D, R, and A connected by segments with given lengths: CA = 36 m, SR = 13 m, DR = 48 m, SD = 7 m, and now the length

1. **Stating the problem:** We have a polygon with points C, S, D, R, and A connected by segments with given lengths: CA = 36 m, SR = 13 m, DR = 48 m, and SD = 7 m. We need to find

1. **State the problem:** We have a diamond-shaped quadrilateral ABCD with diagonals AC and BD intersecting at right angles (90°). Given: $AC=10$, $DB=17$, and angle near vertex A

1. **State the problem:** We have a diamond-shaped quadrilateral ABCD with given side lengths and algebraic expressions for sides.

1. **State the problem:** We need to determine if the triangles EFG and TUV are right-angled using Pythagoras' theorem. 2. **Recall Pythagoras' theorem:** For a triangle with sides

1. **State the problem:** We need to find the length of side $XY$ in a right-angled triangle $XYZ$ where angle $Y$ is the right angle. 2. **Identify the sides:** The hypotenuse is

1. **Stating the problem:** We are given a quadrilateral ABCD with diagonals AC and DB intersecting at right angles. The lengths of AC and DB are given as 10 and 17 respectively, a

1. **Stating the problem:** Calculate the length of the mid-segment (midline) MN of trapezoid ABCD, where M and N are midpoints of sides AB and CD respectively.

1. **State the problem:** Find the volume of a cylinder with height 6, width 12, and length 4. 2. **Identify the formula:** The volume $V$ of a cylinder is given by the formula:

1. **State the problem:** Given parallelogram ABCD with $m\angle DAC = 28^\circ$, $m\angle DCA = 25^\circ$, $AD = 18$, $AB = 10$, and $BE = 8$ on diagonal $BD$, find $m\angle ABC$

1. **State the problem:** We are given two similar triangles ABE and CDE with corresponding sides AB = 93 ft, BC = 98 ft, CE = 68.6 ft, and we need to find the length $d = ED$. 2.

1. **State the problem:** We have two similar right triangles \(\triangle NML \sim \triangle KMO\). Given sides are \(NL = 15\) m, \(ML = 12\) m, \(OM = 16\) m, and we need to find

1. **State the problem:** Calculate the surface area of a cylinder with height $h=10$ cm and diameter $d=6$ cm. 2. **Formula for surface area of a cylinder:**