📐 geometry

1. **State the problem:** Calculate the surface area of the given prism with edges labeled as 4 cm, 8 cm, 13 cm, 7 cm, 12 cm, and 18 cm. 2. **Formula for surface area of a prism:**

1. **State the problem:** We need to find how many identical square-based pyramids Liam can paint completely with 7460 mm² of paint. 2. **Identify the dimensions:** The pyramid has

1. **State the problem:** Calculate the surface area of a triangular prism with triangular base sides $16$ mm, $25$ mm, and base $33$ mm, height of the triangle $12$ mm, and prism

1. **State the problem:** Calculate the surface area of a pyramid with a square base edge of $6$ cm and a slant height of $13$ cm. 2. **Formula for surface area of a pyramid:**

1. **State the problem:** We are given that $m\angle MON=74^\circ$ and need to find $m\angle KJR$ using the diagram. 2. **Analyze the diagram and angles:** The two diagonal lines i

1. **State the problem:** We need to find the angle congruent to $\angle DCM$ based on the given diagram and markings. 2. **Analyze the diagram:** The angle $\angle DCM$ is marked

1. **Problem Statement:** We have an isosceles triangle $\triangle ABC$ with $BM$ as the median to side $AC$. The ratio $BM : AC = 1 : 2$. We need to determine which statement abou

1. **State the problem:** Show that the quadrilateral with vertices $W(1,4)$, $X(1,8)$, $Y(-3,9)$, and $Z(-3,3)$ is a trapezoid and determine if it is isosceles. 2. **Recall the tr

1. **Problem Statement:** Construct a parallelogram $PQRS$ where side $PQ = 5.8$ cm, side $PS = 4.5$ cm, and diagonal $QS = 6.2$ cm. 2. **Important Properties:**

1. **State the problem:** We need to find the value of $t$ in rectangle PQRS where the sides are labeled as follows: - Side $SP = 7t - 72$

1. **State the problem:** We need to find the value of $a$ in rhombus $EFGH$ where angle $E = a$ and angle $G = 2a - 70^\circ$. 2. **Recall properties of a rhombus:** Opposite angl

1. **State the problem:** We are given a circle with center $O$, chords $AH$ and $BC$ which are parallel, and segments $OG$ and $OH$ of equal length. We need to find the size of an

1. **State the problem:** We have two perpendicular planes $X$ and $Y$. Points $A$, $E$, $F$, and $G$ lie only in plane $X$. Points $R$ and $S$ lie in both planes $X$ and $Y$. Line

1. **State the problem:** We have two pairs of parallel lines: $a \parallel b$ and $e \parallel f$. Angles $(x + 1)^\circ$, $y^\circ$, and $(x - 3)^\circ$ are given at intersection

1. The problem asks to name the angle $\angle IJK$ in three different ways. 2. The angle $\angle IJK$ has vertex at point $J$, and is formed by rays $JI$ and $JK$.

1. **Problem Statement:** We are asked to find two other ways to name the angle $\angle n$.

1. **Problem 11:** Seven unit squares are aligned edge-to-edge forming a rectangle of dimensions $7 \times 1$. The diagonal $PQ$ of this rectangle is drawn. We need to find the rat

1. **Problem Statement:** Given triangle $ABC$, points $D$ on $BC$, $E$ on $AC$, $M$ midpoint of $AB$, and $N$ midpoint of $DE$. Given $BD = AE$. The segment $MN$ is extended to in

1. **State the problem:** Sean and Daniela observe a quadrilateral $WXYZ$ with diagonal $WZ$. They note that $\angle 1$ at vertex $W$ and $\angle 2$ at vertex $Z$ are congruent. Se

1. **Problem Statement:** Find the measure of angle 5 in the given figure where parallel horizontal and vertical lines are cut by a diagonal transversal. 2. **Understanding the fig

1. **State the problem:** We need to find the value of $k$ given two angles $(2k+3)^{\circ}$ and $(4k-3)^{\circ}$ that together form a right angle. 2. **Understand the geometry:**