Question

Please help me i really want to know the answerand the explanation for this problems​

Answer 1

Answer:

M = 4.33885225095

Step-by-step explanation:

Area of the square ABFE = 10² = 100

M = 100 - (2P + Q)

Let’s calculate 2P + Q :

The area 2P + Q = area ΔABC + area of sector ACE + area of sector BCF

Note :

ΔABC is an equilateral triangle

m∠CBF = m∠CAE = 30°

area ΔABC  = (CG × AB)÷2 = (8.660254037844×10)÷2 = 43.30127018922

CG = √(10^2 - 5^2)=8.660254037844  (Pythagorean theorem)

area of sector BCF = area ΔACE = 100π ÷ 12 = (8.333333333333)π

then

Area 2P + Q = area  ΔABC + area sector ACE + area sector BCF

                      = 43.30127018922+(100÷12)π+(100÷12)π

                      = 43.30127018922+ (8.333333333333)π + (8.333333333333)π

                      = 95.66114774905

Conclusion:

M = 100 - (2P + Q) = 100-95.66114774905 = 4.33885225095