📐 geometry

1. **Problem statement:** Find the area of the trapezoid at bottom-left. 2. **Formula for trapezoid area:**

1. **Problem Statement:** Given triangle ABC with segment DE parallel to BC and segment EF parallel to AB, and given lengths BC = 24, AC = 18, AB = 18, DE = 6, EF = 12, determine w

1. **Stating the problem:** We are given two triangles, \(\triangle DEF\) and \(\triangle ABC\), with \(\angle F \cong \angle C\) and right angles at \(D\) and \(A\) respectively.

1. **State the problem:** Find the angle $\angle XYZ$ in the given right triangle with vertices $X$, $Y$, and $Z$. 2. **Identify the sides:** From the description, the triangle $XY

1. **State the problem:** We need to find the height $h$ of a tree that casts a shadow 10 feet long, with the distance from the top of the tree to the end of the shadow being 26 fe

1. **State the problem:** We need to find the length of the cable, which forms the hypotenuse of a right triangle with legs 12 feet (flagpole height) and 6 feet (distance from base

1. **Problem:** Points A, B, and C are collinear. Given distances AB and BC, find AC. 2. **Formula:** Since points are collinear, the distance AC is the sum of AB and BC:

1. **Problem statement:** Prove the Pythagorean Theorem using the method of arranging four right-angled triangles inside a square. 2. **Given:** Four right-angled triangles with le

1. **State the problem:** Prove the Pythagorean Theorem using the method of arranging four right-angled triangles around a square of side length $c$. 2. **Formula and rules:** The

1. **Stating the problem:** Calculate the area of the shape described in Question 11 with dimensions 8 mm, 2 mm, and 17 mm.

1. **Problem statement:** Calculate the scaled dimensions and the front area of a hexagonal house drawn at a scale of 1:200.

1. **Problem statement:** In parallelogram ABCD, point X lies on BC such that $\angle BAX = \angle CAD$ and the ratio $AX : AC = 5 : 7$. Given $XB = 100$, find $CX$. 2. **Formula a

1. **Problem:** Diana is painting a circular mural with a diameter of 7 feet. Find the area she will paint. 2. **Formula:** The area $A$ of a circle is given by

1. The problem asks to identify the abscissa and ordinate of point C on a Cartesian coordinate system. 2. The abscissa is the x-coordinate (horizontal position), and the ordinate i

1. **Problem Statement:** Find the measures of angles and arcs in circles where the vertex of the angle lies on the circle. 2. **Key Formula:** For an angle with vertex on the circ

1. **Stating the problem:** Mia, David, and Carla combined their free rectangles to form a new shape with sides measuring 8 inches, 2 inches, 5 inches, 3 inches, another 5 inches,

1. **State the problem:** We are given that segment BD bisects segment AC, meaning BD divides AC into two equal parts at point D. 2. **Identify given lengths:** AB = 8, BC = 7, DC

1. **State the problem:** Jaxon has two boxes. The first box has dimensions length = 24 inches, width = 12 inches, and height = 10 inches. The second box keeps the same length and

1. The problem is to find the length of the third side (hypotenuse) of a right triangle with legs 3 and 4. 2. Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are

1. **State the problem:** We have a right triangle with one leg of length 6 and the hypotenuse of length 10. We need to find the length of the other leg. 2. **Formula used:** In a

1. **State the problem:** We have a right triangle \(\triangle GHI\) with \(\angle I = 90^\circ\), \(\angle G = 59^\circ\), and the leg adjacent to \(\angle G\) (side \(h\)) is 67