Question

Areas ofthetrianglesareasfollows:a1=1024,a2=1016,a3=1057. Whatistheareaofa4?

Answer 1

Answer:

The area of a4 is 1065 .

Step-by-step explanation:

As we know

a1 = a x h1 / 2 .........(a)  

a3 = a x h2 / 2 .........(b)  

where h1 + h2 = b

1- Now find h2 by subtracting h1 from b

 h2 = b - h1

2- Put the value of h2 in equation ...(b)

1024 = a x h1 / 2              

1057 = a x ( b - h1 ) / 2

3- Multiply both sides of the above equations by 2  

2048 = a x h1                   2114 = a b - a h1  

Therefore:

 2114 = a b - 2048

ab = 2048 + 2114 = 4162

4-  Total area of the rectangle is A(total) = a b

a4 = A(total) - ( a1 + a2 +a3 ) = 4162 - ( 1024 + 1016 + 1057 )  

= 4162 - 3097 = 1065