📐 geometry

1. **Problem statement:** Given trapezium ABCD with E and F as midpoints of non-parallel sides AD and BC respectively, prove that line segment EF is parallel to AB and that its len

1. **State the problem:** We have a triangle with side lengths in the ratio 2 : 6 : 7, and the longest side is 24.5 cm. We need to find the perimeter of the triangle. 2. **Understa

1. **Masalah Kapal Berlayar:** Diketahui kapal berlayar ke utara sejauh 80 km dan ke timur sejauh 192 km. Ditanya jarak terpendek (sisi miring) dari posisi awal ke posisi akhir. 2.

1. **Problem statement:** We have a rhombus with each side length $15$ cm and an area of $40$ cm$^2$. We need to find the angles of the rhombus. 2. **Formula used:** The area of a

1. **Problem statement:** Find the distance between the two lines \(l_1\) and \(l_2\) given by: \(l_1:\) \(x = t, y = t, z = t, t \in \mathbb{R}\)

1. **Problem Statement:** Prove that triangles $\triangle FGH$ and $\triangle IJH$ are congruent. 2. **Given Information:**

1. **Problem statement:** We have two congruent triangles, $\triangle ABC$ and $\triangle ABD$. Given: $AC=10$, $AB=6$, $\angle BAC=53^\circ$, $\angle ACB=37^\circ$, $BC=8$ (perpen

1. **Problem Statement:** We need to find the lengths of the sides labeled $x$ in the given figure. 2. **Formula and Rules:** Typically, to find unknown side lengths labeled $x$, w

1. **Problem statement:** Three rods k, l, and m of equal length are fixed at a common point. Rods k and m are perpendicular, and rod l lies between them.

1. **Problem Statement:** Given a parallelogram REST with angles at vertices T, S, R, and E labeled as $x$, $y$, $45^\circ$, and $80^\circ$ respectively, find the values of $x$, $y

1. **Problem statement:** We need to find the length of edge $AD$ in a triangular pyramid with given angles and side $BC = 37$ cm. 2. **Given data:**

1. **Problem Statement:** Calculate the length of edge $AD$ in the given triangle-based pyramid, where angles at $D$, $A$, and $B$ are $39^\circ$, $44^\circ$, and $126^\circ$ respe

1. **Problem statement:** We have a circle with points P, Q, and R on its circumference. RT is a tangent at R and is parallel to chord PQ. Given PR = 8 cm and \(\angle QRT = 70^\ci

1. **Problem statement:** Given triangle ABC with sides AB = 18, BC = 24, and CA = 20. Point D is on AB such that AD = 15, and point E is on BC such that EC = 20. Lines AE and DC i

1. **Problem Statement:** Find the perimeter of trapezoid ABCD where AB is parallel to DC.

1. **Problem statement:** Given a circle with center $O$ and points $Q$, $R$, and $P$ on the circumference, where $OR = OP$ and $OQ = PQ$, and the central angle $\angle QOR = 70^\c

1. **State the problem:** We need to find the area of a circle with radius $r = 6$ miles. 2. **Formula:** The area $A$ of a circle is given by the formula:

1. **State the problem:** We need to find the area of a circle given its diameter is 14 kilometers. 2. **Formula:** The area $A$ of a circle is given by the formula $$A = \pi r^2$$

1. The problem states that the diameter $d$ of a circle is 8 centimeters, and we need to find the area of the circle rounded to the nearest hundredth. 2. Recall the formula for the

1. **Problem statement:** Find the perimeter of polygon ABCD where $m(\angle B) = m(\angle ACD) = 90^\circ$, $AB = 4$ cm, $BC = 3$ cm, and $AD = 13$ cm.

1. **State the problem:** Chu needs carpet for a square room with an area of 15 m². The carpet rolls are 3.8 m wide. We need to determine if the carpet can cover the room without s