Find the surface area and volume of tetrahedron with 2 in ed

Find the surface area and volume of tetrahedron with 2 in. edges. The shown net forms a regular square pyramid with all lateral and base edges the same length. Find the following: slant height l = _______ Base Perimeter P = ______ Base Area B = ______ Lateral Area L = ______ Surface Area S = ______

Solution

Q(10)

1. Area of the whole surface of the regular tetrahedron

= sum of the areas of four congruent equilateral triangles.

= 4 (3)/4 a²

= 3 a² square units;

= 3*(2)² inch²

= 43 inch²

2. Volume of the regular tetrahedron

= 1/3 × area of the base × height

= (1/3) (3)/4 a² × (2)/(3) a

= (2/12) a³ cubic units.

= (2/12)* (2)³

= (2/12)*8

= 22/3 Inch³

Q(11)

Base Perimeter: Since it is a square at the base of side 2 inches, the perimeter is 4* side= 4*2= 8 inches

Base Area: Since it is a square at the base of side 2 inches, the area is (side)²= (2)²= 4 inch ²

Lateral Area: The Lateral area of a square pyramid is given by adding the areas of each of the 4 triangular faces(all equilateral triangles of area (3)/4 a²

= 4* (3)/4 a²

=4* (3)/4* (2)²

=4* (3)/4*4

=4 3 inch²

Surface Area: The Surface area of the square Pyramid is the sum of its Base area and the area of the 4 equilateral triangle. Simply Speaking SA= Base Area+Lateral Area

We know that the lateral area = 4 3 and the Base area(which is a square)= a²= 2*2= 4

Therefore the Surface area = (4+43) inch²