Answer:
Step-by-step explanation:
a). Since, BC is perpendicular to the plane FEDC, measure of angle BCD = 90°
By applying Pythagoras theorem in ΔBCD,
BD² = BC² + CD²
BD² = (10)² + (24)²
BD = √676
BD = 26 cm
B). Surface area of the wedge = Sum of all the surfaces of the wedge
Area of BCD = Area of AEF = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(10)(24)[/tex]
= 120 cm²
Area of CDEF = Length × Width
= ED × CD
= 26 × 24
= 624 cm²
Area of BCFA = 10 × 26 = 260 cm²
Area of ABDE = ED × BD
= 26 × 26
= 676 cm²
Total surface area of the wedge = 2(120) + 624 + 260 + 676
= 1800 cm²
C). Volume of the triangular prism = Area of the triangular base × Height
= (Area of BCD) × DE
= 120 × 26
= 3120 cm³
d). By applying sine rule in the right triangle BCD,
sin(∠BDC) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{BC}{BD}[/tex]
m(∠BDC) = [tex]\text{sin}^{-1}(\frac{10}{26})[/tex]
= 22.6°