Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
A man moves from point $T$ 12 km due West and then 12 km due South to point $Q$. We need to find the...
TrigonometryBearingRight Triangles
2025/4/11
A solid brass cube with height $h$ is melted and recast as a solid cone of height $h$ and base radiu...
VolumeCubeConeGeometric FormulasAlgebraic Manipulation
2025/4/11
We are given a rhombus with diagonals of length 12 cm and 5 cm. We need to find the perimeter of the...
RhombusPerimeterDiagonalsPythagorean Theorem
2025/4/11
The problem is to find the measure of angle $XZT$ in triangle $XYZ$, where side $XY$ is equal to sid...
TriangleIsosceles TriangleAngle PropertiesExterior Angle Theorem
2025/4/11
We are given a right triangle $LMN$ with $|LM| = 6$ cm, $\angle LMN = 90^\circ$, $\angle LNM = x$, a...
TrigonometryRight TriangleAreaSineTangentPythagorean Theorem
2025/4/11
The sum of the interior angles of a regular polygon with $k$ sides is given as $(3k - 10)$ right ang...
PolygonsInterior AnglesExterior AnglesRegular PolygonsAngle Sum Formula
2025/4/11
We are given a diagram where $\angle ABC$ and $\angle BCD$ are right angles. We are also given that ...
AnglesQuadrilateralsParallel LinesSupplementary Angles
2025/4/11
We are asked to find the area of the largest rectangle that can be inscribed in the ellipse given by...
EllipseOptimizationAreaCalculus
2025/4/11
We are given an ellipse with equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a \neq b$. We ...
EllipseTangentsAnalytic GeometryCoordinate GeometryQuadratic Equations
2025/4/11
We are asked to find the area of the largest rectangle that can be inscribed in the ellipse given by...
EllipseOptimizationCalculusAreaRectangle
2025/4/11