📐 geometry

1. **Problem statement:** We have a net of a rectangular pyramid with a diamond shape split into four triangles by two perpendicular dashed lines. The vertical dashed line is 11 yd

1. **Problem Statement:** Find the surface area of a square pyramid given its net. The net consists of a square base with side length 10 m and four congruent triangular faces each

1. **State the problem:** We are given the area of a circle as $36\pi$ square inches and need to find the circumference in terms of $\pi$. 2. **Recall formulas:**

1. **State the problem:** We need to find the volume of a rectangular prism with side lengths $\frac{3}{4}$ cm, $\frac{1}{5}$ cm, and $\frac{5}{7}$ cm. 2. **Formula for volume of a

1. **Problem statement:** Two parallel lines $u$ and $v$ are cut by a transversal $f$. Given $m \angle 1 = 70^\circ$, find the measures of angles 2 and 3 and identify their relatio

1. **State the problem:** Calculate the volume of a rectangular prism with length $14$ ft, width $9$ ft, and height $5$ ft. 2. **Formula:** The volume $V$ of a rectangular prism is

1. The problem asks to find the lines of symmetry for a regular hexagon and select all that apply from lines l, m, n, and o. 2. A regular hexagon has 6 lines of symmetry: 3 lines p

1. The problem asks us to complete the statement about the congruence of triangles after a reflection across the y-axis. 2. Reflection across the y-axis is a type of rigid transfor

1. The problem asks for the translation rule that maps the line segment VW to V'W'. 2. The original segment VW is vertical at $x = -9$ from $y = 10$ to $y = 3$.

1. **State the problem:** We have a line segment VW with endpoints approximately at $(-2,8)$ and $(-2,0)$. 2. The translated line segment V'W' has endpoints approximately at $(-8,-

1. The problem asks to identify the correct congruence statement between two triangles, △XYZ and △NQP, based on their vertex labels and side markings. 2. Congruent triangles have c

1. **State the problem:** We have four points: (2, 6), (-2, 5), (-3, -10), and (3, 3). Each point undergoes a translation defined by the rule $(x, y) \to (x - 8, y + 4)$. 2. **Form

1. **State the problem:** We have triangle ABC with points A(0,4), B(0,0), C(4,0) and its image A'B'C' with points A'(5,7), B'(5,3), C'(9,3) after a translation. We need to find th

1. The problem involves three triangles with given angles and side lengths. We need to analyze the first triangle with angles 90°, 40°, 50° and sides 13 cm, 5 cm, 12 cm. 2. Recall

1. **Problem:** Determine if the given sets of three angle measures can be the angles of a triangle. 2. **Rule:** The sum of the interior angles of a triangle must be exactly $180^

1. **Problem Statement:** Find the value of angle $z$ given that it is adjacent to an angle measuring $34.1^\circ$ and the two angles are formed by perpendicular lines. 2. **Unders

1. **State the problem:** We are given two rhombuses and need to find their perimeter ($P$) and area ($A$).

1. Let's first state the problem: We need to find the area and perimeter of problem 3. 2. Since the problem details are not provided, let's assume problem 3 refers to a rectangle w

1. The problem is to find the area and perimeter of a given shape. 2. The formulas for a rectangle are:

1. The problem asks to find the perimeter and area of a rhombus with side length 10.7 ft and one diagonal 8 ft. 2. The perimeter $P$ of a rhombus is given by the formula:

1. **Problem statement:** Find the perimeter and area of the right triangle with sides 9 cm, 12 cm, and 5 cm, and height 3.4 cm. 2. **Perimeter formula:** The perimeter $P$ of a tr