📐 geometry

1. **Problem Statement:** Calculate the area of each triangle and trapezoid given their dimensions. 2. **Formula for Area of Triangle:**

1. **State the problem:** We have two rectangles with the same perimeter. The green rectangle has width 11 mm and height 18 mm. The orange rectangle has height 4 mm and an unknown

1. **State the problem:** We have two rectangles with the same perimeter. One rectangle has dimensions 14 ft by 2 ft, and the other is a purple square with side length 7 ft. We nee

1. **State the problem:** We have two rectangles with the same perimeter. The first rectangle has sides 19 km and 17 km. The second rectangle has one side 15 km and the other side

1. **State the problem:** We need to find the perimeter of a sector of a circle where the arc length is 21 cm and the central angle is 120 degrees. 2. **Recall the formula for the

1. **Problem Statement:** We need to find the scale factor to reproduce a blueprint so that its area becomes 45 square inches and it fits on a standard sheet of paper. 2. **Underst

1. **Problem Statement:** (a) Find the size of angle $\angle ACB$ in triangle $ABC$ where $BC=AC=7$ cm.

1. The problem asks to find the bearing of Liverpool from London given the bearing of London from Liverpool is 130°. 2. Bearings are measured clockwise from the north direction. Th

1. **Problem Statement:** We have several geometry problems involving triangles and polygons with given side lengths and angles. We will solve for areas, side lengths, and angles s

1. **Problem Statement:** Given a diagram with two parallel lines cut by a transversal, find the unknown angles $x$, $y$, and $z$ using properties of corresponding angles, interior

1. **State the problem:** We need to find the measure of angle $\angle GMK$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the angles:**

1. **Problem Statement:** We need to find the measure of angle $\angle GMK$ given two expressions for angles related by parallel lines and a transversal. 2. **Given:**

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((2x + 122)^\circ\) and \((154 - 2x)^\circ\). We need to

1. **State the problem:** We need to find the measure of angle $\angle MON$ given two algebraic expressions for angles formed by intersecting lines. 2. **Identify the angles:** The

1. **Problem Statement:** We need to find the measure of angle $\angle QWU$ given two angles formed by a transversal crossing two parallel lines: one angle at point $V$ is $(100 -

1. დავიწყოთ 4.1-ით: წრფოს განზომლა ორ წერტილს შორის არის მანძილი, რომელსაც ვთვლით ფორმულით: $$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

1. **Problem Statement:** We are asked to identify and draw two lines of symmetry for each given shape: a rectangle, an ellipse, a circle with a diagonal line, and a capsule shape.

1. **Problem statement:** We need to find the size of angle $\theta$ in an isosceles triangle where the two equal sides each measure 5.9 cm and the base measures 4.6 cm. The angle

1. **Problem statement:** We need to find the size of the vertex angle $\theta$ in an isosceles triangle where the two equal sides each measure 5.9 cm and the base measures 4.6 cm.

1. **Nyatakan masalah:** Diberi segi tiga OAB dengan titik O(0,0), A(2,-2), B(6,4), dan titik Q(4,1) pada garis AB. Garis OB mempunyai persamaan $y=\frac{2}{3}x$. Titik P terletak

1. **Problem statement:** We have points $X(0,0)$, $Y(7,24)$, and $Z(15,0)$. Point $W$ lies on segment $YZ$ such that $\angle WXZ = 3 \times \angle WXY$. We need to find the coordi