Question

Find the perimeter and area of each figure.

Answer 1

`\sf\\a.\ Solution:\\Perimeter\ of\ triangle(P)=12+9+5=26units\\Area\ of\ triangle(A)=(1)/(2)* base\ * height=(1)/(2)* 12* 4=24sq. units`

`\sf\\b.\ Solution:\\Area\ of\ parallelogram(A)=base*\ height =10*6=60cm^2\\Perimeter\ of\ parallelogram(P)=10+7+10+7=34cm`

`\sf\\c.\ Perimeter\ of\ rectangle(P)=2(l+w)=2(45+35)=160m\\Area\ of\ rectangle(A)=lw=45* 35=1575m^2`

The question no. a. is technically wrong. This is because there are two formulas for the area of triangle. The one is that we used above and the other one is heron's formula. By using the heron's formula, you get the area of triangle = 4√26 units which is not possible.

Here is the process:

`\sf\\Semi-perimeter(s)=Perimeter/2=13units\\\textsf{Let a, b and c be the sides of the triangle. Let a = 9, b= 12 and c=5.}\\\textsf{Now,}\\\textsf{Using heron's formula,}\\Area\ of\ triangle=√(s(s-a)(s-b)(s-c))=√(13(13-9)(13-12)(13-5))\\=4√(26)sq. units`