📐 geometry

1. **Stating the problem:** We have a right triangle with one leg labeled $b$, the other leg labeled $a$, and the hypotenuse labeled $c=6$. We want to find the values of $a$ and $b

1. The problem is to graph triangle $\triangle FGH$ and its image reflected across the lines $x = -1$ and $y = 1$. 2. Reflection across a vertical line $x = a$ changes a point $(x,

1. **Stating the problem:** We have two shapes on squared paper. We need to enlarge each shape by the given scale factors: (a) scale factor $\frac{1}{2}$ and (b) scale factor $4$.

1. **Stating the problem:** We are given three angles: $ (4x + 15)^\circ $, $ (30x - 5)^\circ $, and $ (20x + 45)^\circ $. Lines BCD and AFE are straight lines, and we need to show

1. **State the problem:** We are given points on a line segment with conditions: B is the midpoint of segment HAC, AC = CD, AB = 3x + 4x, AC = 11x - 17, and DE = 49. We need to fin

1. **Problem 9:** Given points D, E, F are collinear with segments DE and EF such that $DE = 7x + 1$ and $EF = 4x - 3$, and the total segment $DF = 42$. Find $DE$. 2. **Formula:**

1. **State the problem:** Find the volume of the oblique cylinder with given dimensions: base radius $r=5$, height $h=10$, and slant angle $40^\circ$. 2. **Formula for volume of a

1. **Problem statement:** We have a right triangle ABC with right angle at A, where AB = 6 cm and AC = 8 cm. AM is the altitude from A to hypotenuse BC, and BM = MC, so M is the mi

1. **Stating the problem:** We have a right triangle with legs 32 and 2, and inside it a smaller right triangle with legs labeled $a$ and $b$. We need to analyze the given values f

1. **Problem:** The volume of the prism is 2,688 cubic units. Find the missing side $x$ given the sides 8 units, 10 units, and 12 units. 2. **Formula:** Volume of a prism = Base Ar

1. **State the problem:** We need to find the missing dimension $x$ of a rectangular prism given its volume $V = 2736$ cubic inches, and two known dimensions: 24 inches and 1 foot.

1. **State the problem:** Quadrilateral LMNO is similar to quadrilateral PQRS. We are given sides OL = 7, ON = 10, and SP = 32. We need to find the length of side RS. 2. **Recall t

1. **State the problem:** We have two similar triangles ABC and DEF. We know sides CB = 17 and CA = 10.1 in triangle ABC, and side FE = 54 in triangle DEF. We need to find side FD

1. **State the problem:** We have a rectangular garden that is 45 ft wide and 70 ft long. On a drawing, the width is represented as 9 inches. We need to find the length on the draw

1. **State the problem:** We have a triangle that is originally 4 inches tall and 3 inches wide. It is enlarged so that its height becomes 8 inches. We need to find the new width.

1. **State the problem:** We need to find the area of a four-lobed shape formed by four semicircles each with radius $0.5$ cm arranged around a central square, with the total heigh

1. **State the problem:** We need to find the area of a shape composed of a square and a semicircle, both with side/radius length 6 cm. 2. **Formula for area of square:** The area

1. The problem is to understand how to find the areas of triangles and rectangles. 2. The formula for the area of a rectangle is $$\text{Area} = \text{length} \times \text{width}$$

1. **State the problem:** We need to find the area of a compound shape made of a rectangle and a right-angled trapezoid and check if Rio's answer of 4.42 cm² is correct. 2. **Conve

1. **State the problem:** We are given a cone with total surface area $3584\pi$ cm², radius $r=14x$, and height $h=24x$. We need to find the volume of the cone to the nearest integ

1. **State the problem:** We have a right triangle KLM with a right angle at L. The side KL measures 3.1 units, LM measures $x$ units, and KM is the hypotenuse.