📐 geometry

1. **State the problem:** We are given the sum of the interior angles of a polygon as 1620° and need to find the number of sides of the polygon. 2. **Formula:** The sum of the inte

1. **State the problem:** We are given five angles of a hexagon and need to find the measure of the sixth angle. 2. **Recall the formula:** The sum of the interior angles of a poly

1. **State the problem:** We have a right triangle with sides 7.7, 11, and the hypotenuse labeled as $x$ and 10 (likely a typo, we consider $x$ as the hypotenuse). 2. **Identify th

1. **State the problem:** We need to find the surface area of a triangular prism with given side lengths. 2. **Identify the dimensions:** The triangular base has sides 5 m (height)

1. **State the problem:** We are given three points: $A(-3,4)$, $B(2,1)$, and $C(-4,-5)$. We need to find a fourth point $D(x,y)$ such that $ABCD$ forms a kite. 2. **Recall kite pr

1. **Stating the problem:** We have two similar isosceles triangles ABC and DAB with AB = AC and AD = BD. We know the ratio of sides BC to CD is 4:21. We need to find the ratio AB

1. **State the problem:** Susan has a round cake with a diameter of 20 cm. She wants to put a ribbon around the cake. We need to find the least length of ribbon required. 2. **Form

1. **State the problem:** Calculate the length on a scale drawing in centimeters for an actual length of 60 meters with a scale of 1:15.

1. **Problem statement:** Given the number line with points B at -3, O at 0, I at 1, and A at 4, and the line \(\Delta\) defined by points (0, I).

1. **State the problem:** We need to find the surface area of a cylinder with radius $r=4$ and diameter $d=15$. 2. **Recall the formula:** The surface area $A$ of a cylinder is giv

1. **Problem Statement:** Prove that triangles $\triangle HGI$ and $\triangle CID$ are congruent given: - $\angle HGI \cong \angle CID$

1. **State the problem:** We have an unshaded rectangle with perimeter 10 cm, height 3 units, width 2 units, and a larger shaded rectangle formed by joining two copies of the unsha

1. **State the problem:** We need to find the area of the shaded section of a trapezium with a smaller right triangle inside it. 2. **Identify the shapes and dimensions:**

1. **Problem statement:** Calculate the length $x$ in the given triangle with angles 70°, 20°, and side lengths 7 and 4. 2. **Formula used:** Use the Law of Sines: $$\frac{a}{\sin

1. **State the problem:** We need to find the coordinates of point $X$ on segment $CD$ such that the area of triangle $AXD$ equals the area of triangle $BXC$. 2. **Set up the probl

1. **State the problem:** We are given two triangles ABC and DEC where AB is parallel to DE, and the triangles are similar. We need to find the length of AB. 2. **Recall the proper

1. **State the problem:** We have two similar triangles ABC and DEF. We know the sides of triangle DEF: DE = 9 cm, EF = 6 cm, and the sides of triangle ABC: BC = 3 cm, AB = x cm. W

1. **Problem statement:** Aiden and May each place rocks on their side of a river and measure distances to a tree on the opposite bank. We need to determine if their triangles are

1. **State the problem:** Find the total surface area of a combined solid made by joining a triangular prism on top of a parallelogram prism along a congruent rectangular face.

1. **State the problem:** A knight moves forward 3.6 cm from the center of one square to another, then moves diagonally across to the center of the destination square. We need to f

1. **State the problem:** We have a right triangle with vertices A, B, and a third vertex. The side opposite angle $\alpha$ at vertex B is $d=24$, the hypotenuse (side opposite the