📐 geometry

1. **State the problem:** Find the area of the shaded sector of a circle where the central angle $m\angle WOX = 60^\circ$ and the radius is 5 ft. 2. **Formula for the area of a sec

1. **Nyatakan masalah:** Diberikan dua sektor bulatan berpusatkan O, sektor ORQ dengan jejari 12 cm dan sektor OPS dengan jejari 5 cm. Panjang tali busur PQ = 5 cm. Diberi sudut se

1. **State the problem:** We have a right-angled triangle ABC with angle ABC = 90°. AB = 5.3 cm (base, horizontal), BC = 4.8 cm (vertical), both correct to 2 significant figures.

1. **Stating the problem:** We are given a shape composed of 8 equal squares arranged in a specific pattern. We need to find the area $A$ of this shape. 2. **Formula used:** The ar

1. **Stating the problem:** Determine the area of the first figure, which is a 3×3 square grid where each small square represents 1 square meter. 2. **Formula used:** The area $A$

1. **State the problem:** We are given two angles at point B formed by line segments BA, BC, BD, and BE. The angle between BA and BC is $2x+7$ degrees, and the angle between BD and

1. **State the problem:** We are given two angles at point H: $m\angle 2 = (\alpha + 15^\circ)$ and $m\angle 3 = (\alpha + 35^\circ)$. We need to find the value of $\alpha$ such th

1. **Stating the problem:** We are given a circle with points A, C, D, E, and an angle \(\angle CAE = 24^\circ\) and an arc \(\overset{\frown}{DE} = 83^\circ\). We need to find the

1. The problem asks to find the value of the ratio $\frac{\alpha}{\beta}$ given the angles $\alpha$ and $\beta$ in a geometric figure. 2. Since the figure is a quadrilateral with a

1. The problem is to understand the structure of a circular wheel infographic divided into six colored wedges around a black center circle labeled "Math AI Tools 2026". 2. The whee

1. **State the problem:** We have a rectangle ABCD with vertex A at coordinates $(1,4)$. 2. **Transformation rule:** The transformation is a reflection across the line $y = x$.

1. **Stating the problem:** We need to find the measure of angle $\angle ECA$ in the given circle with points $E$, $C$, $D$, $A$, and $B$. 2. **Given information:**

1. **Stating the problem:** We need to find the area of the shaded circular segment (tembereng) in circle O with radius $21$ cm.

1. **State the problem:** (i) Find the volume of a spherical ice cube of radius 1.5 cm in terms of $\pi$.

1. The problem asks if any additional information is needed to show that triangles $\triangle DEF$ and $\triangle GHJ$ are congruent by SAS (Side-Angle-Side). 2. SAS congruence req

1. **Nêu bài toán:** Cho tam giác ABC vuông tại A, có đường trung tuyến BN. Qua N kẻ đường thẳng song song với BC cắt AB tại M. Qua M kẻ đường thẳng vuông góc với AB cắt BC tại D,

1. The problem involves finding the unknown side length $x$ in right triangles using the Pythagorean theorem. 2. The Pythagorean theorem states that in a right triangle with legs $

1. **Problem statement:** Calculate the percentage change in the volume of a prism with a square base of side length $a$ and height $h$ when

1. **State the problem:** We have a large stained glass window and a smaller scale drawing of it. The actual window has an area of 680 m². We need to find the area of the scale dra

1. **State the problem:** We have two similar shapes, C and D.

1. **Stating the problem:** We have a square with side length $R=20$ cm. Inside the square, a diagonal arc runs from the upper-left corner to the lower-right corner, and the angle