📐 geometry

1. **Problem statement:** Given a right isosceles triangle ABE with hypotenuse AE = 10 cm, find the area of the square whose side is the leg BE of the triangle. 2. **Formula and ru

1. **Problem statement:** We have points A, B, C, D, and E on a circle with given angles 26°, 52°, and 125°, and unknown angles $x$ and $y$. We need to find $x$ and $y$. 2. **Key r

1. **State the problem:** We have three identical rectangles arranged in an L-shape on a coordinate plane. The bottom-left corner of the lower rectangle is at $(2,3)$ and the top-r

1. **State the problem:** We are given a quadrilateral with three angles labeled as 110°, 110°, and 70°, and we need to determine if this quadrilateral is a parallelogram. 2. **Rec

1. **State the problem:** We are given expressions for segments SU and SW in terms of $b$ and need to find the value of $b$ that makes quadrilateral TUVW a parallelogram. 2. **Reca

1. **Problem statement:** Given a regular quadrilateral pyramid $S.ABCD$ with base side length $a$ and center $O$. Points $M$ and $N$ are midpoints of edges $SA$ and $BC$ respectiv

1. **State the problem:** We need to find the areas of three parts: (a) the rectangle, (b) the triangle, and (c) the whole composite shape.

1. **State the problem:** We are given the circle equation $$4x^2 + 4y^2 - 8x - 12y + 1 = 0$$ and a point $$P(3, 2.5)$$ outside the circle. We need to find the length of the tangen

1. Soalan: Hitung perimeter kawasan berlorek dalam rajah (a). 2. Formula perimeter segmen bulatan: $$P = 2r + r\theta$$ di mana $r$ ialah jejari dan $\theta$ dalam radian.

1. The problem asks: How and why can a shape be both a kite and a rectangle? 2. Let's define the properties of each shape:

1. Let's start by stating the problem: Can a shape be both a trapezoid and a kite? What are the conditions for each shape? 2. Definitions:

1. **Problem statement:** Find the length of segment $AF$ on trapezoid $DEFG$ where $\angle DEF = 90^\circ$, bases $DE = 6$ and $EF = 30$ are parallel, height $DE = 20$, and point

1. **Problem:** Find the volume and surface area of a cuboid with dimensions 12 cm × 5 cm × 3 cm. 2. **Formulas:**

1. **Problem statement:** Find the angle $x$ in each diagram where two parallel lines are cut by a transversal, and a known angle is given on the opposite parallel line. 2. **Key r

1. **Problem statement:** Find the area of the shaded parts in a figure composed of two adjacent semicircles, each with radius 2 cm. The left semicircle is divided vertically into

1. **Problem statement:** We have two circles with centers $C$ and $D$ and radii 8 and 10 units respectively. The distance between centers $CD$ is 14 units. The circles intersect a

1. The problem states that three angles formed at the center of a circle add up to 360° because the total degrees around a point is 360°. 2. The given angles are 152°, 49°, and $x$

1. **Problem Statement:** Three solid spheres with diameters $\frac{3}{2}$ m, 2 m, and $\frac{5}{2}$ m are melted and combined to form a new solid sphere. We need to find the diame

1. **Problem statement:** We need to find the length of side $FG$ in a right triangle $FGH$ where the right angle is at vertex $F$. The sides $FH$ and $HG$ are given as 6 cm and 15

1. **State the problem:** We need to find the volume of a right-angled triangular prism. The triangle face has sides 23 m and 38 m (hypotenuse), and the prism depth (length) is 11

1. Let's start by understanding the problem: you want to find an angle corresponding to a given percentage. 2. A percentage can be thought of as a part of a whole, and when relatin