Question

Find the volume and surface area of this shape

Answer 1

171.65

Explanation:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving forA

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=5·10+5·10+5·10+1

2·﹣54+2·(5·5)2+2·(5·5)2﹣54+2·(5·5)2﹣54≈171.65064

Answer 2

Surface area = 184 cm²

Volume = 120 cm³

Explanation:

1) Formula to find the surface area of a triangular prism is:

Surface area = ( Areas of the 3 rectangles) + ( Area of the 2 triangles)

Let us solve it now.

Surface area = ( Areas of the 3 rectangles) + ( Area of the 2 triangles)

= ( 10 × 6 + 10 × 5 + 10 × 5 )cm² + ( 2 × 1/2 × 6 × 4 ) cm²

= ( 60 + 50 + 50 ) cm² + 24 cm²

= 160 cm² + 24 cm²

= 184 cm²

2) Formula to find the volume of the triangular prism is:

Volume = Area of the cross section × length

Let us solve now.

Volume = Area of the cross-section ( area of the triangle ) × length

= 1/2 × b × h × l

= 1/2 × 6 × 4 × 10

= 120 cm³