📐 geometry

1. **State the problem:** Suzie's pool dimensions are given as 6 feet deep, 7 feet wide, and 4 feet long. We need to find the capacity of the pool. 2. **Formula used:** The capacit

1. **Problem statement:** A sheet of A4 paper (297mm x 210mm) is folded once and then laid flat. We need to determine which of the given shapes (a square/rectangle, triangle, tall

1. **Problem:** The base of the triangular pyramid is equilateral and has an area of approximately 5.1 cm². Find the total surface area of the triangular pyramid. 2. **Formula and

1. **State the problem:** We have two similar pentagons, A (smaller) and B (larger). We know the side lengths of pentagon A: 10 cm, 12 cm, 15 cm, 6 cm, and 9 cm. For pentagon B, th

1. **State the problem:** We have a right triangle with a vertical leg of length 10 inches and a horizontal leg of length 8 inches. We want to analyze or find properties related to

1. **State the problem:** We have trapezoid PQST with \overline{ST} parallel to \overline{PQ}. Given lengths are \(RQ=36\), \(RT=22.5\), \(PR=24\), and \(PQ=32\). We need to find t

1. **State the problem:** We have two triangles with a pair of parallel sides: TU is parallel to QR. Given QR = 15, TU = 10, and QS = 9, we need to find the length of TS. 2. **Use

1. **State the problem:** Find the area of a trapezoid given its bases and height. 2. **Formula:** The area $A$ of a trapezoid is given by

1. **State the problem:** Find the area of the given shape with sides 9 ft, 6 ft, 17 ft, and 4 ft. 2. **Analyze the shape:** The shape appears to be a quadrilateral. To find its ar

1. **State the problem:** We need to find the value of the angle $x$ in a circle where two secants intersect outside the circle, creating angles labeled $20^\circ$, $104^\circ$, an

1. The problem asks to identify which two triangles are congruent by the SAS (Side-Angle-Side) Theorem and complete the congruence statement. 2. The SAS Theorem states that if two

1. **State the problem:** We have triangle XYZ with sides XY = 5 cm, XZ = y cm, YZ = x cm, and angle \(\angle X = 60^\circ\). Given \(x = y - 1\), find the perimeter \(k\) of the t

1. **Problem statement:** Find the area of each trapezoid given the bases and height. 2. **Formula for the area of a trapezoid:**

1. **Problem Statement:** Find the missing leg length in a right triangle given one leg and the hypotenuse. 2. **Formula:** Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $

1. **State the problem:** Circle all triangles congruent to the first triangle in the row.

1. **State the problem:** We are given that triangles \(\triangle ABC\) and \(\triangle EDC\) are similar, and we need to find the distance \(x\) across the bay, which corresponds

1. **State the problem:** We are given an arc length expression $6 + 12x$ and an angle of $45^\circ$ at point $X$ on a circle. We need to solve for $x$. 2. **Relevant formula:** Th

1. Let's start by stating the problem: You want to find the area using a formula and then divide the result by 4. 2. The general area formula depends on the shape, but for example,

1. **State the problem:** We are given a circle with points Q, P, and R on its circumference. The angle at point P formed by chords QP and PR is 75°. 2. **Given:** The arc QP measu

1. **Problem statement:** We have a greenhouse framework with a cross-section shaped as a quarter-circle of radius 4 metres. The length of the greenhouse (depth) is 8 metres.

1. **State the problem:** We have a circle with chords WX, XS, WV, and diameter XV passing through the center. The angle at point X between diameter XV and chord XS is 52°. 2. **Go