Basics of Quadrilateral

In a quadrilateral ABCD, with unequal sides if the diagonals AC and BD intersect at right angles, then _____

If the three angles of a quadrilateral are $120°, 130°, 10°$ then what is the fourth angle ?

Which of the following is pair of opposite sides in the given figure.

The vertical angles of two isosceles triangles are same and the ratio of their areas is $9:16$. Then the ratio of their heights is:

If the area of equilateral triangle is $10\sqrt{3} {\mathrm{cm}}^2$, then the length of the median is:

$2 \mathrm{cm}$ of rain has fallen on a square km of land. Assuming that $50\%$ of the raindrops could have been collected and contained in a pool having a $100 \mathrm{m} \times 10 \mathrm{m}$ base, by what level would the water level in the pool have increased?

ABCD is a quadrilateral with AB parallel to DC and AD parallel to BC.$\angle ADC$ is a right angle. And E is point DC such that $\Delta AEB$ is an equilateral triangle. If the perimeter of the triangle ABE is$6 units$, what is the area of the quadrilateral?

If a solid cone of volume $27\mathrm{\pi } {\mathrm{cm}}^3$ is kept inside a hollow cylinder whose radius and height are that of the cone, then the volume of water needed to fill the empty space is:

What is the sum of the measures of angles of a convex quadrilaterals?

Inside a square $ABCD, \Delta BEC$ is an equilateral triangle. If  $CE$ and $BD$ intersect at $O$, then $\angle BOC$ is equal to____

If the length and the perimeter of a rectangle are in ratio $5:16$, then its length and breadth will be in the ratio _____.

The vertex angle of an isosceles triangle measures ten times the measure of a base angle. Find the measure of the base angle?

In the figure given above, $\mathrm{O}$ is the centre of the circle,$\mathrm{OA}=3 \mathrm{cm}, \mathrm{AC}=3 \mathrm{cm}$and $\mathrm{OM}$ is perpendicular to $\mathrm{AC}$. What is $\angle \mathrm{ABC}$ equal to?

If $I$ is the incentre of $∆\mathrm{ABC}$ and $\angle BIC=135°$, then find $∆\mathrm{ABC}$.

A circle is inscribed inside an equilateral triangle touching all the three side. If the radius of the circle is $2 cm$. Find the area of triangle

A cube of edge $5 \mathrm{cm}$ is cut into cubes each of edge $1 \mathrm{cm}$. Find the ratio of the total surface area of one of the small cubes to that of the large cube.

The tangents drawn at P and Q on the circumference of a circle intersect at A. If$\angle \mathrm{PAQ}$ is $68°$ , then the measure of $\angle \mathrm{APQ}$ is equal to______.

A school has carpentry as a vocational education course for the boys after grade $10$. A boy cut a plywood as shape given above. The instructor asked him to make a report as given below.

The shape of the plywood cut is

This polygon is a :

This shape is a: