Answer:
x = 12
Step-by-step explanation:
The midsegment VY is half the sum of the parallel bases , that is
VY = , then
3x + 18 = (x + 96) ← multiply both sides by 2 to clear the fraction
6x + 36 = x + 96 ( subtract x from both sides )
5x + 36 = 96 ( subtract 36 from both sides )
5x = 60 ( divide both sides by 5 )
x = 12
42 square units
<h2>Step-by-step explanation:</h2>For a better understanding, I add an EFGH Rectangle.
The area of EFGH Rectangle = p x l
The area of EFGH Rectangle = 10 x 8
The area of EFGH Rectangle = 80cm²
The area of BHA Triangle = 1/2 x a x t
The area of BHA Triangle = 1/2 x a x t
The area of BHA Triangle = 1/2 x 6 x 4
The area of BHA Triangle = 2 x 6
The area of BHA Triangle = 12cm²
The area of AGD Triangle = 1/2 x a x t
The area of AGD Triangle = 1/2 x 4 x 2
The area of AGD Triangle = 4cm²
The area of CFD Triangle = 1/2 x a x t
The area of CFD Triangle = 1/2 x 2 x 6
The area of CFD Triangle = 6cm²
The area of BEC Triangle = 1/2 x a x t
The area of BEC Triangle = 1/2 x 8 x 4
The area of BEC Triangle = 4 x 4
The area of BEC Triangle = 16cm²
The area of the trapezoid = EFGH Rectangle - (BHA Triangle + AGD Triangle + CFD Triangle + BEC Triangle)
The area of the trapezoid = 80 - (12 + 4 + 6 + 16)
The area of the trapezoid = 80 - 38
The area of the trapezoid = 42cm²
<h3>Conclusion :</h3>The area of the trapezoid is <u>42 square units</u>
