Geometry

Problems related to shapes, spaces, measurements, etc.

Problems in this category

Show that $\vec{a} \times (\vec{b} \times \vec{a}) = (\vec{a} \times \vec{b}) \times \vec{a}$.

Vector AlgebraVector Triple ProductVector OperationsCross ProductDot Product
2025/6/17

The problem asks to find the area $S$ of a sector with radius $r = 4$ and arc length $l = 10$.

SectorAreaArc LengthGeometric Formulas
2025/6/17

The problem asks to identify the prism that can be formed from the given nets. We are given four dif...

PrismsNets3D ShapesCubesRectangular PrismsTriangular PrismsCylinders
2025/6/17

The problem asks to identify the prism formed by the given nets. The image shows four nets. The firs...

3D ShapesNetsPrismsCylindersCube
2025/6/17

We are given a triangle with one exterior angle of $130^\circ$ and one interior angle labeled as $x$...

TrianglesAnglesExterior AnglesInterior Angles
2025/6/17

We are given a triangle with two of its angles known. Angle A is $85^\circ$ and angle B is $68^\circ...

TrianglesAngle Sum PropertyLinear Equations
2025/6/17

We are given a circle with center O. CD is a tangent to the circle at point C. Angle CDB is given as...

CircleTangentAnglesAlternate Segment TheoremIsosceles Triangle
2025/6/17

The problem asks us to find the gradient of the line passing through each of the given pairs of poin...

Coordinate GeometrySlopeGradientLinear Equations
2025/6/17

We are given a pentagon with some information about its angles and sides. We need to find the size o...

PolygonsPentagonsAnglesIsosceles Triangle
2025/6/17

We are given a triangle with one exterior angle of $249^\circ$. Two of the interior angles of the tr...

TrianglesInterior AnglesExterior AnglesAngle Sum Property
2025/6/17