📐 geometry

1. **Calculate angle EAC in the first pyramid:** The base ABCD is a square with side $AB=5$ cm.

1. The problem states that triangle ABC is right angled at B, so by the Pythagorean theorem, the squares of the two sides around angle B sum to the square of the hypotenuse AC. Tha

1. **State the problem:** We are given a quadrilateral with points P, Q, R, and S such that angles PQS and RQS are right angles ($90^\circ$). Lengths $PS=5.3$ cm, $PQ=3.8$ cm, and

1. Stating the problem: We have a triangle intersected by two parallel lines, with angles given as 87°, 45°, and 36°, and we need to find the size of angle $x$. 2. Identify paralle

1. Problem statement. We are given a rectangular ground floor of width $15$ m and height $20$ m, divided into three stacked rectangles: a top garage of dimensions $15\times4$, a mi

1. Problem 21: Find the equation of the circle with center at (2, 3) and radius 5. The general form of a circle's equation is $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $ (h, k) $ is

1. দেওয়া দুটি বিন্দু হল P(4, 11) এবং Q(-2, 2)। আমরা PQ সরল রেখার লম্ব সমবাহুরকের সমীকরণ নির্ণয় করব। 2. প্রথমে PQ সরলরেখার ঢাল নির্ণয় করি। ঢালের সূত্র হলো:

1. **Stating the problem:** We have a right-angled triangle $\triangle ABC$ with the right angle at vertex $A$. The line segment $AD$ is perpendicular to $BC$. We need to find whic

1. **Problem Statement:** We have two equilateral triangles each with side length 8 cm. We want to join these two triangles to form a quadrilateral and identify the type of quadril

1. **Problem Statement:** (a) Place two rubber bands perpendicular to each other, forming diagonals of equal length and join the ends. Identify the quadrilateral.

1. We are given two similar rectangles. The dimensions of the first rectangle are 8 cm by 12 cm. 2. Since the rectangles are similar, their corresponding sides are proportional.

1. **State the problem:** We have two similar trapezoids, Shape A and Shape B. Given dimensions:

1. Given that PQRS is a rectangle with sides PQ = 2 m, QR = 3 m, and PS = 6 m, we first clarify the dimensions. Since PS should be equal to QR, let’s assume PQRS is a rectangle wit

1. The problem states that PQRS is a rectangle with lengths PQ = 2 m + 6 m = 8 m and QR = 3 m. We need to find the area of the shaded region which excludes a rectangular notch at t

1. The problem asks: Which angles are congruent to $\angle 2$? - $\angle 2$ is an alternate interior angle with $\angle 6$ (because lines $m$ and $n$ are parallel and cut by the tr

1. **State the problem:** We need to find (i) the area of the quadrilateral site ABCD with given side lengths and angles, and (ii) the volume of soil excavated for a ditch 40 m lon

1. We are given triangle ABC with angles $\angle B = 72^\circ$, $\angle A = 50^\circ$, and side $AC = 18.7$ cm opposite angle B. 2. (a) To find length $BC$, we first determine angl

1. **Find the value of $n$ in the triangle with angles 112°, 100°, and $n$.** The sum of angles in any triangle is $180^\circ$.

1. **State the problem:** We want to find the area of a right triangle with legs each measuring $\frac{1}{2}$ mile and compare it to the total area of 50 football pitches.

**Problem 1: Triangle OGA angles** 1. Given: $m\angle OGA = 76^\circ$, $m\angle AG = 160^\circ$.

1. **State the problem:** We have a tetrahedron (triangular pyramid) with a vertical height of 9 meters and a base that is an equilateral triangle with side length 7 meters. 2. **R