*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon:
square units
(22)
Similar to (21)
Area =
square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:


Hence, area of the hexagon will be:
square units
(24)
Given is the inradius of an equilateral triangle.

Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle =
square units
Answer:

Step-by-step explanation:

Let's apply the formula (x+y)² = x² + 2xy + y²
Here, x = -a and y = b
So,
= (-a)² + 2(-a)(b) + (b)²
= a² - 2ab + b²
Hence, it has been proved that (-a + b)² = a² - 2ab + b².
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
Answer:
In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis).
Step-by-step explanation:
When you divide exponents, you have to subtract them. So -4-3= -7 as the exponent
When you have a negative exponent, then you have to flip the fraction (all whole numbers are over 1 so flip the 1 to the top and the 5^7 on the bottom)
Answer:
and 
and b=
Step-by-step explanation:
We are given that a quadratic equation

We have to solve the equation by completing square and find the value of b.






and 

And 
Therefore,
and 
and b=