Question

Which big these flags will have the greatest area? Why?

Answer 1

Question 1:

The area of flag b is the greatest.

Explanation:

Area of triangle = $\frac{1}{2}base*height$

Area of parallelogram = base * height

For flag A:

It is a triangle with base = b and height = a

Area of flag A = $\frac{1}{2}a*b$ square units

For flag B:

It is a parallelogram with base = a and height = b

Area of flag B = a*b square units

For flag C:

It is a triangle with base = b and height = a

Area of flag C = $\frac{1}{2}a*b$ square units

From the above, we can conclude that the area of the parallelogram (flag B) is the greatest

Question 2:

The perimeter of flag C is shorter than that of flag A

Explanation:

Perimeter is the sum of the three sides of the figure

For flag C:

The three sides are given as a, b and c

Therefore, perimeter of flag c = a + b + c units

For flag A:

We are given two sides as b and c and we are given that the height is a

We know that in the given flag, the third side (the unknown slant one) will be longer than the height of the height of the triangle

Therefore, the third side = a + k where k is a constant

Therefore, perimeter of flag A = a + b + c + k units

From the above, we can conclude that the perimeter of flag C is shorter

Hope this helps :)