Hey there :)
All these shapes are known as a rhombus.
The are formula of a rhombus is [tex] \frac{(side1)(side2)}{2} [/tex]
1st ) The area is given = 48 in²
The diagonals are 1) 8 in and 8 in = 16 in , 2) x in and x in = 2x in
Apply the formula to find x
[tex] 48=\frac{(16)(2x)}{2} [/tex]
48 = 16x
Divide by 16 on either side to isolate x
[tex] \frac{48}{16}= \frac{16x}{16} [/tex]
3 = x
Check:
Area = [tex] \frac{(8+8)(3+3)}{2} [/tex]
= [tex] \frac{96}{2} [/tex]
= 48 in²
2nd ) Area is given = 48 ft²
The diagonals are 1) 4 + 4 = 8 ft , 2) x
Apply the formula to find x
48 = [tex] \frac{(8)(x)}{2} [/tex]
48 = 4x
Divide by 4 on either side
[tex] \frac{48}{4} = \frac{4x}{4} [/tex]
12 = x
Check:
Area = [tex] \frac{(4+4)(12)}{2} [/tex]
= [tex] \frac{96}{2} [/tex]
= 48 ft²
3rd ) Given diagonals are 19 ft and 38 ft
Area = [tex] \frac{(19)(38)}{2} [/tex]
= [tex] \frac{722}{2} [/tex]
= 361 ft²
