1. What is the base edge of the prism in cm?
Let the sides of the triangle are a,b,c and angles are α,β,γ . The formula of a triangle area by two sides and the angle between them is:
S=1/2∗a∗b∗sinγ.
In equilateral triangle sides are equal a=b=c and angles are equal. Each angle has 60o. So,
S(base)=1/2∗a2∗sin(60o),a2=2∗S(base)/sin(60o),a2=2∗1560/0.866==3602.77(cm2),a=√3602.77=60.023(cm).
Answer: 60.023(cm).
2. What is the lateral area of the prism in m2?
Let the attitude of the prism is
d.d=5m.a=60.023cm=0.6m.
A prism's lateral area is equal to one of its bases perimeter times its height:
S(lateral)=P∗d,P=3∗a=3∗0.6=1.8(m),S(lateral)=1.8m∗5m==9(m2).Answer:9(m2).
3. What is the volume of the prism in m3?
V=S(base)∗d,V=0.156m2∗5m=0.78(m3).Answer:0.78(m3).
Comments