📐 geometry

1. **State the problem:** Find the surface area of a right circular cone with height $19$ cm and base radius $3$ cm, using $\pi = 3.14$. 2. **Formula for surface area of a cone:**

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula:** The standard form of a circle's equation with center $(h,

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula:** The standard form of a circle's equation with center $(h,

1. The problem asks to measure the angles of four polygons: two triangles (a-b-c and d-e-f) and two quadrilaterals (g-h-i-k and m-n-o-p) using a protractor, and then to draw and me

1. **State the problem:** Calculate the surface area of a triangular prism with triangular base sides 4 in, 5 in, and 6 in, and height (length) 3 in.

1. **State the problem:** We have a rectangle with length 32 cm and width 14 cm. Two semicircles, each with diameter 14 cm, are cut out from the shorter sides. We need to find the

1. **State the problem:** We have a rectangular paperboard measuring 27 inches long and 22 inches wide. A semicircle with diameter equal to the width (22 inches) is cut out from th

1. **State the problem:** We have two triangles, △ABC and △DEF, with given sides and angles: $AB=15$, $BC=20$, $\angle B=37^\circ$, $DE=24$, and $\angle E=37^\circ$. We want to fin

1. **Problem statement:** Given two parallel lines $a \parallel b$ and a transversal, with an angle of $120^\circ$ at the upper intersection and expressions $7x - 10$ and $10y - 10

1. **Problem Statement:** Determine whether the triangles in problem 9 are similar by AA~, SSS~, SAS~, or not similar. 2. **Given:** Two triangles connected by segment UW with angl

1. **State the problem:** Find the surface area of the composite L-shaped figure made of two rectangular prisms joined perpendicularly. 2. **Identify dimensions:**

1. **State the problem:** Find the volume of the composite figure composed of two rectangular prisms joined together. 2. **Identify dimensions:**

1. Problem: If J is the circumcenter of \(\triangle DEF\), find the length of \(DH\). Given segments: \(EG = 8x - 17\), \(GF = 6x - 7\), and \(JH = 8\). 2. Since \(J\) is the circu

1. **State the problem:** We have two right triangles, ABC and ACD, with given angles and some side lengths. We need to find the missing sides $k$, $m$, $x$, and $y$. 2. **Triangle

1. **Problem:** Find the perimeter of a kite with sides 12 and 20. 2. **Formula:** Perimeter of a kite = 2 × (sum of lengths of two distinct adjacent sides).

1. **State the problem:** We are asked to find the measure of angle $\angle F$ in the circle with center $O$, given $m\angle DOE = 72^\circ$ and $m\angle EOG = 84^\circ$, and $EF$

1. **State the problem:** We are given angles formed by rotating vectors \(\overrightarrow{AB}\) and \(\overrightarrow{CD}\) to create angles \(\angle XPA\) and \(\angle XPC\) with

1. **State the problem:** We are given that $m\angle WXZ = 95^\circ$ and $m\angle 1$ is 27° more than $m\angle 2$. We need to find $m\angle 2$. 2. **Understand the angles:** $\angl

1. **Problem Statement:** Given three sets of parallel lines: $a \parallel b$, $c \parallel d$, and $e \parallel f$, and the segments with lengths 12, 5, and 8, find the missing si

1. **Problem Statement:** Draw the preimage and image of triangle PQR under a translation along the vector $\langle -1, 3 \rangle$. The triangle vertices are $P(1, -3)$, $Q(3, -1)$

1. **Problem Statement:** Translate quadrilateral ABCD along the vector \(\langle -4, -6 \rangle\).