Answer:
The answer to your question is 92.4 cm²
Step-by-step explanation:
Data
Side of a square = 6 units
Longest side of a rhombus = 10 units
Process
1.- Calculate the area of the square
Area = 6 x 6 = 36 u²
2.- Calculate the area of the rhombus
-Calculate the length of the short diagonal
6² = x² + x²
6² = 2x²
36 = 2x²
18 = x²
x = √18
-Short diagonal
x = 2√18
-Calculate the length of the long diagonal
10² = (√18)² + b²
b² = 100 - 18
b² = 82
b = √82
-Length of the long diagonal
d = √82 + √18
-Area of the rhombus
Area = (√82 + √18)(2√18) / 2
Area = (√82 + √18)(√18)
3.- Calculate the total area
Total area = (√82 + √18)(√18) + 36
-Simplification
Total area = (13.298)(4.243) + 36
Total area = 56.418 + 36
Total area = 92.4 cm²
