📐 geometry

1. **State the problem:** We have two similar quadrilaterals. We know the lengths of some sides and need to find the missing length $q$ in the smaller figure. 2. **Identify given l

1. **State the problem:** We have two similar quadrilaterals. The left quadrilateral has a bottom side of 60 mm and a right side of 40 mm. The right quadrilateral is similar, with

1. **State the problem:** We have two similar quadrilaterals. The side lengths of the larger one are 40 mm and 60 mm, and the smaller one has a side length of 42 mm and a missing s

1. **State the problem:** We have two similar quadrilaterals. The first has angles 45°, 135°, 135°, and 45°. We need to find the missing angle in the second similar figure. 2. **Re

1. **State the problem:** We have two similar figures with corresponding side lengths. We need to find the missing length $v$ in the yellow figure. 2. **Recall the property of simi

1. **State the problem:** Find the area of the composite figure consisting of a rectangle with dimensions 9 ft by 8 ft, a semicircle attached on the left side with diameter 8 ft, a

1. **Problem:** Solve for $x$ given two parallel lines cut by a transversal with angles $51^\circ$ and $7x + 9$ as alternate interior angles. 2. **Formula and rule:** Alternate int

1. **Stating the problem:** Beräkna arean av segmentet i figuren där triangelns höjd är markerad. 2. **Formel och regler:** Arean av ett cirkelsegment kan beräknas med formeln

1. **State the problem:** We have two similar cones, Cone A and Cone B.

1. **State the problem:** We have two similar pyramids with base edges 16.5 m and 22 m. 2. **Find the scale factor (a:b) of their corresponding linear dimensions:**

1. **State the problem:** We need to find the surface area of a cylindrical soup can with radius $AB = 2.7$ cm and height $BC = 10.9$ cm. 2. **Formula for surface area of a cylinde

1. **State the problem:** We need to find the surface area of a cylindrical display stand with radius $AB = 7.8$ cm and height $BC = 21.1$ cm. 2. **Identify the formulas:**

1. **State the problem:** We need to find the surface area of a cylindrical display stand with radius $AB = 7.8$ cm and height $BC = 21.1$ cm. 2. **Recall formulas:**

1. **State the problem:** We are given a cone with sides AB = 20.7 feet (radius), BC = 81.9 feet, and CA = 84.5 feet (slant height). We need to find the surface area of the cone us

1. **State the problem:** We need to find the surface area of a square pyramid with base side length $AD = 18.7$ feet and slant height $EG = 25.71$ feet. 2. **Formula for surface a

1. **State the problem:** We need to find the surface area of the salt shaker top, which is a square pyramid with base side length $AD = 20$ mm and slant height $EG = 7.76$ mm. 2.

1. The problem states that a right circular cylinder has a radius $r$ inches and height $h$ inches, and its volume is given as 10 cubic inches. 2. The formula for the volume $V$ of

1. **State the problem:** We have triangle RST with sides RS = 5, TS = 9, and angle \(\angle S = 87^\circ\). We need to find \(m\angle R\), side \(s = RT\), and \(m\angle T\). 2. *

1. **State the problem:** We are given a triangle with vertices Y, W, and X, and side lengths $YW=7$, $WX=9$, and $YX=12$. We need to find the measures of angles $\angle W$, $\angl

1. **State the problem:** We need to find the volume of soil dug out to make a cylindrical well with depth (height) $21.5$ m and diameter $5$ m. 2. **Formula for volume of a cylind

1. **State the problem:** We need to find the volume of soup that fits in a cylindrical can with radius $r=3$ cm and height $h=7$ cm. 2. **Formula:** The volume $V$ of a cylinder i