📐 geometry

1. **State the problem:** We have a compound L-shaped figure made of two rectangles. The total area is given as 75 cm². We need to find the value of $x$, the width of the upper rec

1. **State the problem:** We have an L-shaped compound figure with total area 92 cm². The total width is 10 cm, total height is 8 cm. The top horizontal segment is 4 cm, the vertic

1. **State the problem:** We have a triangle with points A, C, B and a segment AD inside it, where AD = 64 units and DB = 28 units. On the base CB, segments CE = 20.7 units and EB

1. **State the problem:** We need to find the missing side length $x$ of a rectangle where the area is 29 square inches and the other side length is 7.5 inches. 2. **Formula for th

1. **Problem Statement:** The base of the lampshade is a regular hexagon with side length 8 inches. We need to estimate the amount of glass needed to make the lampshade, which mean

1. **Problem 9:** Find the surface area of a regular pyramid with base length 10 yd and slant height 7.8 yd. 2. **Formula:** Surface area $SA = B + \frac{1}{2}Pl$ where $B$ is base

1. **State the problem:** Find the coordinates of point P on the line segment connecting the black checker at (2,5) and the white checker at (7,8) such that the ratio of the distan

1. **Problem:** Find the coordinates of point P along the directed line segment ST so that the ratio of SP to PT is 1 to 3, where S = (6, 4) and T = (-4, -8). 2. **Formula:** To fi

1. **Stating the problem:** We have a parallelogram with the top side length 27 cm and the right side length 18 cm. The left side is labeled $c$ and the bottom side is labeled $d$.

1. Let's first define the types of angle pairs mentioned: - Supplementary angles: Two angles whose measures add up to $180^\circ$.

1. **State the problem:** We need to find the area of an L-shaped figure composed of two rectangles. 2. **Identify the rectangles:**

1. **State the problem:** We have a parallelogram with an interior angle $a = 48^\circ$. We want to find the values of $a$ and $b$.

1. **State the problem:** We need to find the total area of a compound figure made of two rectangles stacked vertically. 2. **Identify the dimensions:**

1. **Problem Statement:** Given angles in a diagram with four intersecting lines forming 14 angles, find the measures of angles 2, 4, 5, 6, 7, 8, 9, 11, 13, and 14 using the given

1. **State the problem:** We have a rectangle JKLM with given angles and side lengths. We need to find the length JK. 2. **Recall properties of rectangles:** In a rectangle, opposi

1. **Problem Statement:** We have a rectangle JKLM with sides ML = 30 units and KL = 18 units. The angles given are 59° and 72°, and we need to find the length JK. 2. **Recall prop

1. The problem asks to describe the translation from triangle ABC to triangle A'B'C'. 2. Translation moves every point of a figure the same distance in the same direction.

1. The problem asks for the sum of the interior angle measures of a polygon that is a triangle. 2. The formula for the sum of interior angles of any polygon with $n$ sides is:

1. **Problem Statement:** Estimate the measure of angle $\angle WXY$ formed at point $X$ by segments $WX$ and $XY$. 2. **Understanding the angle:** The angle $\angle WXY$ is the an

1. The problem asks for the sum of the interior angle measures of a triangle. 2. The formula for the sum of interior angles of any polygon with $n$ sides is:

1. The problem asks to find the image of the parallelogram GRAM after a translation 11 units right and 2 units up. 2. Translation rule: To translate a point $(x,y)$ by $a$ units ri