Arun Sharma Solutions for Exercise 3: Extra Practice Exercise on Geometry and Mensuration

If the sides of a triangle measures 13, 14, 15 cm respectively, what is the height of the triangle for the base is 14.

A right angled triangle is drawn on a plane such that sides adjacent to right angle are $3 cm$ and $4 cm$. Now three semi-circles are drawn taking all three sides of the triangle as diameters respectively (as shown in the figure). What is the area of the shaded regions $A_1+A_2$

In the figure given below, $AB=16, CD=12$ and $OM=6$. Calculate $ON$.

In the figure, $M$ is the centre of the circle. $1\left(QS\right)=10\sqrt{2}$ , $1\left(PR\right)=1\left(RS\right)$ and $PR$ is parallel to $QS$. Find the area of the shaded region.

In the given figure, $PBC$ and $PKH$ are straight lines. If $AH=AK$, $b={70}^o, c={40}^o$, the value of $d$ is

Six solid hemispherical balls have to be arranged one upon the other vertically. Find the minimum total surface area of the cylinder in which the hemispherical balls can be arranged, if the radii of each hemispherical ball is $7 \mathrm{cm}.$

On a semicircle with diameter $AD,$ Chord $BC$ is parallel to the diameter. Further each of the chords $AB$ and $CD$ has Length $2 \mathrm{cm}$ while $AD$ has length $8 \mathrm{cm}.$ Find the length of $BC.$

In the given figure, $B$ and $C$ are points on the diameter $AD$ of the circle such that $AB = BC = CD.$ Then find the ratio of area of the shaded portion to that of the whole circle.