(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
