📐 geometry

1. **State the problem:** We need to find the area of a trapezium with parallel sides of lengths 9 cm and 30 cm, and a height of 8 cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** Calculate the area of a trapezium with top base $12$ cm, bottom base $6$ cm, and height $5$ cm. 2. **Formula for the area of a trapezium:**

1. **State the problem:** We need to name two similar triangles from the given diagram and explain why they are similar. 2. **Identify the triangles:** The triangles mentioned are

1. **Stating the problem:** We have two similar triangles, $\triangle ABC \sim \triangle DBE$. Given side lengths are $AC=10$, $DE=4$, and $BE=3$. We need to find the length of $AB

1. The problem is to find the volume of a cylinder with a base radius of 50 cm and a height of 5 cm. 2. The formula for the volume $V$ of a cylinder is:

1. **State the problem:** We need to find the height $h$ at which the volleyball player hits the ball. The volleyball net is 8 feet tall, the ball lands 15 feet away from the base

1. **State the problem:** We need to find the image of triangle \(\triangle JKL\) under a dilation centered at the origin with scale factor \(\frac{1}{3}\). 2. **Recall the dilatio

1. **State the problem:** We need to find the measure of angle $\angle KML$ in quadrilateral $KJML$ where $\angle J = 108^\circ$ and $\angle MNL = 25^\circ$. 2. **Understand the se

1. The problem asks for the measure of angle $\angle B$ in the hexagon with given interior angles: $\angle A = 120^\circ$, $\angle B = 129^\circ$, $\angle C = 148^\circ$, $\angle D

1. **Problem statement:** Find the value of $x$ in triangle $ABC$ where angles are $x^\circ$ at $A$, $2x^\circ$ at $B$, and $330^\circ$ at $C$. 2. **Formula used:** The sum of inte

1. The problem asks to identify the type of special triangle given one angle of 30° and a right angle (90°). 2. A triangle with angles 30°, 60°, and 90° is a well-known special rig

1. **Problem statement:** We have a right triangle with a hypotenuse $e$, one leg of length $3\sqrt{3}$, and an angle of $60^\circ$ adjacent to that leg. We want to find the length

1. **Problem statement:** We have two similar rhombuses ABCD and ECFA. The diagonals EF and BD measure 4 m and 16 m respectively. We need to find the perimeter of the larger rhombu

1. **State the problem:** We need to find the total volume of wax required to make 110 cylindrical candles, each with diameter 6 inches and height 6 inches. 2. **Formula for the vo

1. **Problem statement:** A cube has a volume of 216 cm³. We need to find:

1. **State the problem:** We are given a right rectangular prism with three face areas: front face area = 39 cm², top face area = 65 cm², and side face area = 15 cm². We need to fi

1. **Stating the problem:** We are given a rectangular prism with dimensions 6 cm, 7 cm, and 12 cm. We want to calculate its volume and surface area.

1. **Problem statement:** A fish pond is a rectangular prism with length 4 m, width 3 m, and depth 2 m.

1. **State the problem:** We have an equilateral triangle $\triangle ABC$ with side length 5 cm.

1. The problem asks if the two triangles can be proved congruent and which postulate can be used. 2. The common triangle congruence postulates are:

1. **Problem statement:** We have a square divided into 4 parts: triangles A and B, and trapeziums C and D. Given: