Question

I need help with this math worksheet

Answer 1

(7)The area of triangle = 0.5 * height * base // height = 6 ft //base = 10 ft //Area = 0.5 * 6 * 10 = 30 ft²===========================================================================
(16)length of the square = 2 * √7 = 2√7  // 
Area of the square = (2√7)² = 28   //
==========================================================================================================
(29) If the length of regular hexagon = a  //  
Apothem of regular hexagon = a sin 60 // 
apothem = 6 // 
∴ the length of hexagon = apothem/ sin 60 = (12√3)/3 //  
perimeter = 6 * the length of hexagon = 24√3 //  
Area = 0.5 * perimeter * apothem = 0.5 * 24√3 * 6 = 72√3 //  

=====================================================(39)  The length of the arc = radius * inscribed angels in radian //   ∴ The length of the arc = 4 * 110 * π/180 = 22π/9 ≈ 7.68 in  //    =======================================================
(45)The shaded area = half the area of the circle - Area of the triangle //     Area of triangle = 0.5 * r² * sin 120 = 0.5 * 6² * sin 120 = 15.588 //   Area of the circle = π r² = 3.14 * 6² = 113.04 //   The shaded area = 0.5 * 113.04 - 15.588 = 40.96  ≈ 41