Q.How will you measure the diameter of the Moon using parallax method?

Direct instruments like a scale or caliper cannot reach the height of a tree, let alone the distance to the Moon or a planet -- these need indirect geometric or wave-based methods.

Triangulation method (for the height of an accessible object): stand at point $C$, a known horizontal distance $x$ from the base $B$ of a tower/tree of height $h=AB$, and measure the angle of elevation $\theta=\angle ACB$ to the top $A$ with a range finder. From the right triangle $ABC$: $\tan\theta=h/x$, so

Parallax method (for the distance of a far-away object like a planet or star): parallax is the apparent shift in an object's position against a distant background when it is viewed from two different points; the separation between those points is the basis, $b$. If the small parallax angle subtended at the object is $\theta$, and $x$ is the (large) unknown distance, treating the basis as a small arc of a circle of radius $x$ gives $\theta=b/x$, so

Application -- distance of the Moon: observe the Moon simultaneously from two diametrically opposite points $A,B$ on Earth (basis $b=AB=$ Earth's diameter), each against the same distant background star; the individual parallax angles $\theta_1,\theta_2$ add to give the Moon's total parallax $\theta=\theta_1+\theta_2$. Since the Earth-Moon distance $MC\approx AM$, $\theta\approx AB/MC$, so $MC=AB/\theta$.

RADAR method (RAdio Detection And Ranging): beam a radio pulse toward a nearby planet and time the round-trip interval $t$ until its echo returns. Since the pulse covers the distance twice (out and back) at the wave speed $v$ (= speed of light):

The same round-trip-timing idea (with the speed of sound instead of light) underlies sonar ranging underwater, and RADAR/sonar-style timing can equally determine the altitude of an aircraft.

Practical distance units that make astronomical numbers manageable: 1 light year $=9.467\times10^{15}$ m (distance light travels in vacuum in one year); 1 astronomical unit (AU, mean Earth-Sun distance) $=1.496\times10^{11}$ m; 1 parsec (distance at which a 1 AU arc subtends a parallax angle of exactly 1 arc-second) $=3.08\times10^{16}$ m $=3.26$ light years. Quoting a star's distance in light years or parsecs, rather than kilometres, avoids writing out an unwieldy number of digits every time.