Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
A rectangle $PQRS$ has dimensions $20$ cm by $(10+10)$ cm $= 20$ cm. A square of side $x$ cm has be...
AreaRectangleSquareProblem with an error
2025/4/20
A rectangle $PQRS$ has dimensions 20 cm by 10 cm. A square of side $x$ cm is cut from each of two co...
AreaRectangleSquareAlgebraic Equations
2025/4/20
The problem describes triangle $XYZ$ with $XY = 10$ cm, angle $YXZ = 40^{\circ}$ and angle $XYZ = 60...
Triangle ConstructionGeometryAnglesSide Lengths
2025/4/20
A rectangle $PQRS$ has dimensions $20$ cm by $(10+10)$ cm $= 20$ cm. A square of side $x$ cm is cut ...
AreaRectangleSquareAlgebraic Equations
2025/4/19
The diagram shows a rectangle $PQRS$ with length $10+10=20$ cm and width $20$ cm. A square of side $...
AreaRectangleSquareAlgebraic Equations
2025/4/19
We are given the coordinates of the vertices of a quadrilateral UVWX: $U(6,-2)$, $V(1,3)$, $W(-7,6)$...
Coordinate GeometryQuadrilateralsSlopeDistance FormulaParallelogram
2025/4/19
The problem asks us to find the coordinates of point $D$ such that points $A(-2, 3)$, $B(2, 8)$, $C(...
ParallelogramCoordinate GeometryMidpoint Formula
2025/4/19
The problem requires converting equations from one coordinate system to another. We will solve probl...
Coordinate SystemsCylindrical CoordinatesSpherical CoordinatesCoordinate Transformations
2025/4/19
We have a circle $PQRS$ with center $O$. We are given that $\angle UQR = 68^\circ$, $\angle TPS = 7...
CirclesCyclic QuadrilateralsAnglesGeometric Proofs
2025/4/19
The problem requires converting equations from rectangular coordinates $(x, y, z)$ to cylindrical co...
Coordinate SystemsCoordinate TransformationsCylindrical CoordinatesSpherical Coordinates3D Geometry
2025/4/19