Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem consists of two parts: (a) A window is in the shape of a semi-circle with radius 70 cm. ...
CircleSemi-circlePerimeterBase ConversionNumber Systems
2025/6/11
The problem asks us to find the volume of a cylindrical litter bin in m³ to 2 decimal places (part a...
VolumeCylinderUnits ConversionProblem Solving
2025/6/10
We are given a triangle $ABC$ with $AB = 6$, $AC = 3$, and $\angle BAC = 120^\circ$. $AD$ is an angl...
TriangleAngle BisectorTrigonometryArea CalculationInradius
2025/6/10
The problem asks to find the values for I, JK, L, M, N, O, PQ, R, S, T, U, V, and W, based on the gi...
Triangle AreaInradiusGeometric Proofs
2025/6/10
In triangle $ABC$, $AB = 6$, $AC = 3$, and $\angle BAC = 120^{\circ}$. $D$ is the intersection of th...
TriangleLaw of CosinesAngle Bisector TheoremExternal Angle Bisector TheoremLength of SidesRatio
2025/6/10
A hunter on top of a tree sees an antelope at an angle of depression of $30^{\circ}$. The height of ...
TrigonometryRight TrianglesAngle of DepressionPythagorean Theorem
2025/6/10
A straight line passes through the points $(3, -2)$ and $(4, 5)$ and intersects the y-axis at $-23$....
Linear EquationsSlopeY-interceptCoordinate Geometry
2025/6/10
The problem states that the size of each interior angle of a regular polygon is $135^\circ$. We need...
PolygonsRegular PolygonsInterior AnglesExterior AnglesRotational Symmetry
2025/6/9
Y is 60 km away from X on a bearing of $135^{\circ}$. Z is 80 km away from X on a bearing of $225^{\...
TrigonometryBearingsCosine RuleRight Triangles
2025/6/8
The cross-section of a railway tunnel is shown. The length of the base $AB$ is 100 m, and the radius...
PerimeterArc LengthCircleRadius
2025/6/8