List of top Quantitative Aptitude Questions on Geometry

If the angle bisector of \( \angle P \) meets \( QR \) at point \( M \), find the length of \( PM \).
An aquarium of size 100 cm × 80 cm × 60 cm is tilted along the 80 cm edge. Water spills until the water line reaches 1/3 of the base width. Find the height of water reduced when box is restored.
If the equations below hold true for triangles ABC and DEF: \[ a(a + b + c) = d^2, b(a + b + c) = e^2, c(a + b + c) = f^2 \] Then which of the following is always true of triangle DEF?
In triangle PQR, \( PQ = 12 \) cm, \( PR = 9 \) cm, and \( \angle Q + \angle R = 120^\circ \). Find the length of QR.
PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:
An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD?
In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.
The semi-circle
There are two solid pyramids, each having 8 edges of length 8 cm each. These two pyramids are moulded to form a hexagonal pyramid with length of each side as 8 cm. What is the slant height of the new pyramid?
In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.
In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is :
AB is the chord of the circle with centre O
In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.
In the figure below, PT and ST are two secants. If O is the centre of the circle and PQ = 2QT = 8 cm, OS = 5 cm, then what is the measure of the line OT? (Figure not drawn to scale)
PT and ST are two secants. If O is the centre of the circle and PQ = 2QT = 8 cm, OS = 5 cm
In triangle PQR, the straight line parallel to side QR meets PQ and PR at points ‘A’ and ‘B’, respectively. If PA = BR, PQ = 36 cm and PB = 6 cm, then BR = ?
In a rectangular coordinate system, triangle ABC is drawn so that one side of the triangle connects two points on the y axis, A(0, 2) and B(0, -4). If point C has coordinates (c, 0) and the area of ABC is 21, then C =
Find the perimeter of Isosceles triangle ABC (below) if mAD = 3 and m\(\angle\)BAC = 55 degrees. Round to the nearest hundredth.

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What would be the circumference of a circle that has been inscribed in a square of area 5.
A square PQRS is enclosed in another square ABCD. Find the ratio of the area of PQRS to the area of ABCD.

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What is the ratio of the area of triangle ABC to the area of square ADFC if CB=(CF)/4?

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s, p and q are interior angles of an Isosceles triangle. Find the value of q.
1. s = 72°.
2. p and q are base angles of the triangle.
Is A an obtuse angle?
1. A is more than 90°.
2. A is a supplement of an angle B, an acute triangle.
Determine the value of angle k.
1. Angle k and m lies on a straight line.
2. Angle m = 39°.
What will be the area of a semi-circle whose perimeter if 12 cm?