📐 geometry

1. **State the problem:** We have a right triangle $\triangle PQR$ with $\angle R = 90^\circ$, $\angle P = 61^\circ$, and side $p = 98$ inches opposite $\angle P$. We need to find

1. **State the problem:** We are given the area of a parallelogram as 36 in² and the height as 9 in. We need to find the length of the base. 2. **Formula for the area of a parallel

1. **State the problem:** We are given a parallelogram with an area of 22 cm² and one side length of 5 cm. We need to find the length of the height corresponding to that side. 2. *

1. **State the problem:** We are given a circle with points E, F, and G on the circumference and two inscribed angles: $\angle E = (12x + 40)^\circ$ and $\angle F = (8x + 10)^\circ

1. **State the problem:** We have triangle ABC with interior angles at A and B given as 97° and 34°, respectively, and an exterior angle at vertex C labeled as $z$. We need to find

1. **State the problem:** Maya wants to find the area of a shaded triangle. She knows the height is 10 m and needs to find the correct base length to use. 2. **Recall the formula f

1. The problem asks for the area of a triangle with a base of 8 units and a height of 6 units. 2. The formula for the area of a triangle is:

1. **Stating the problem:** We are given a geometric figure with several lines and their relationships:

1. The problem asks to determine which statement about the given geometric figure is true based on the angles and lines described. 2. Let's analyze each statement:

1. **State the problem:** We need to find the surface area of a triangular pyramid composed of six triangular faces, with three top triangles each having height 11 ft and three bot

1. The problem asks to identify which diagram is the correct net for a pyramid with a triangular base where each side of the base is 7 ft and the height from the base to the apex i

1. **State the problem:** Calculate the volume of iron in a hollow cylindrical pipe with outer diameter 11 in, thickness 0.45 in, and length 20 in. 2. **Formula used:** Volume of h

1. **State the problem:** We need to find the volume of iron in a hollow cylindrical pipe with outer diameter 11 in, thickness 0.45 in, and length 20 in. 2. **Formula used:** The v

1. **State the problem:** We have a right triangle ABC with a right angle at A, hypotenuse BC = 6, and angle B = 60°. 2. **Identify what to find:** We need to find the lengths AC a

1. **State the problem:** We have an isosceles right triangle (45°-45°-90°) with hypotenuse length 38 inches and need to find the length of side $m$. 2. **Recall the properties of

1. **Problem 1: Find the indicated measures in the circles.** 2. **Arc length of PQ:**

1. **Problem statement:** A right triangle has a horizontal leg measuring 42.7 cm and a hypotenuse measuring 52.5 cm. We need to find the length of the vertical leg. 2. **Formula u

1. **Problem Statement:** Find the length of the missing side in a right triangle using the Pythagorean theorem, given sides $a$, $b$, and hypotenuse $c$.

1. **State the problem:** Determine if points X(3,1), Y(3,7), and Z(11,1) can form a triangle by checking the side lengths and triangle inequality. 2. **Formula for distance betwee

1. **State the problem:** We need to classify triangle $\triangle ABC$ with vertices $A(5,4)$, $B(2,8)$, and $C(6,5)$ based on its angle measures and side lengths. 2. **Find the le

1. **State the problem:** We are given two legs of a right triangle, $a=3$ miles and $b=2.8$ miles, and we want to find the length of the hypotenuse $c$ using the Pythagorean theor