📐 geometry

1. **State the problem:** We need to find the value of angle $x$ in a triangle where two sides and one angle are given. 2. **Given:** Side lengths 5.7, 7, and 7; angles $x^\circ$ (

1. **State the problem:** We have an equilateral triangle with an altitude of length 10, and we need to find the length of side $x$ in simplest radical form with a rational denomin

1. **Problem statement:** Find the length of side $x$ in simplest radical form with a rational denominator in a right isosceles triangle with angles $45^\circ$, $45^\circ$, and $90

1. **State the problem:** We are given a right triangle \(\triangle ABC\) with a right angle at \(C\) and an angle at \(A\) measuring 70°. We need to find the measure of angle \(B\

1. The problem asks which two shapes make up the digital camera shown. 2. The camera body is shaped like a rectangular prism, which is a 3D rectangle.

1. **Problem statement:** Find the measure of angle $x$ given two parallel lines $a \parallel b$ cut by a transversal, with angles $144^\circ$ and $36^\circ$ marked as shown. 2. **

1. The problem asks to find the translation rule that maps the pre-image parallelogram \(\square ABCD\) to the image parallelogram \(\square A'B'C'D'\).\n\n2. Translation moves eve

1. **State the problem:** We are given a triangle \(\triangle A'B'C'\) with vertices \(A'(-1, 2)\), \(B'(-1, -1)\), and \(C'(-4, -1)\) which is the image of \(\triangle ABC\) after

1. **Problem Statement:** Classify point C in a triangle where three medians are drawn to point C from the midpoints of the sides. 2. **Key Concept:** The point where the three med

1. **State the problem:** Solve for $x$ given the angles $(8x - 3)^\circ$ and $(16x - 33)^\circ$ which are part of a triangle, and then find $m\angle CXY$ given angles $48^\circ$ a

1. **State the problem:** We need to find the surface area of a square pyramid with base side length $AD = CD = 1$ mm and triangular face height $EF = 8$ mm. 2. **Understand the sh

1. **State the problem:** We need to find the surface area of a cube where each edge length is given as $AB = 5$ mm. 2. **Formula for surface area of a cube:** The surface area $S$

1. **Find the volume of a prism** Given formula: $$V = Bh$$ where $B$ is the area of the base and $h$ is the height.

1. **Problem:** Find the volume of a rectangular prism with base area $B=112$ and height $h=23$. 2. **Formula:** Volume of a prism is given by $$V = Bh$$ where $B$ is the area of t

1. **Problem Statement:** Given a triangle with a segment parallel to the top side inside it, the top side is 10, the left side is split into 4 and 12, and the inner parallel segme

1. **State the problem:** We need to find the area of the composite shape shown, which is an irregular polygon with sides labeled 9.3 cm, 2 cm, 5 cm, 4 cm, 10 cm, and 6 cm. 2. **Ap

1. The problem is to find the area of the composite stepped polygon with given side lengths: 9.3 cm, 2 cm, 5 cm, 4 cm, 10 cm, and 6 cm. 2. To find the area of a composite shape, we

1. **State the problem:** Identify which segment is a tangent to the circle. 2. **Recall the definition:** A tangent to a circle is a line that touches the circle at exactly one po

1. The problem asks for the volume in cubic units of the given shapes made of unit cubes. 2. Volume of a prism or solid made of unit cubes is the total number of unit cubes it cont

1. **State the problem:** We need to find the surface area of a prism with a pentagonal base having sides 4.7 ft, 7.6 ft, 7.6 ft, 12 ft, and 18 ft. 2. **Formula and rules:** The su

1. **State the problem:** We need to find the total surface area of the roof, which is a pentagonal prism shape with given side lengths 4.7 ft, 7.6 ft, 7.6 ft, 12 ft, and 18 ft. 2.