Given:pyramid with rhombus base with diagonals d sub 1=16 and d sub 2=12 cm., height = 6 cm.?

Question

Compute:
1.base edge of the rhombus
2.slant height MV
3. slant height NV
4.area of lateral face of BCV
5.area of lateral face of ABV
6.area of base
7.total area
8. is the pyramid V-ABCD a regular pyramid?

Answer 1

Given:pyramid with rhombus base with diagonals d sub 1=16 and d sub 2=12 cm., height = 6 cm.?
Compute:
1.base edge of the rhombus
10 cm, Pythagorean triple 6, 8, 10

2.slant height MV
l=√[(24/5)^2+6^2) cm

3. slant height NV
l=√[(24/5)^2+6^2) cm

4.area of lateral face of BCV
(1/2)(10)l, cm^2

5.area of lateral face of ABV
(1/2)(10)l, cm^2

6.area of base
6*8 = 48 cm^2

7.total area
add all faces.

8. is the pyramid V-ABCD a regular pyramid?
No.
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Reasons for 3 and 4:
Let h be the height of 6-8-10 triangle with base 10. By similarity, we have
h/6 = 8/10
h = 24/5 cm

Answer 2

Lets call the height 'h' and the base 'b' Formula for the area of a triangle: Area = base x height -------------------- 2 Base is 6 + 2h Height is h h(6 + 2h) ------------- = 28cm^2 2 Multiply out the brackets 6h + 2h^2 -------------- = 28 2 3h + h^2 = 28 Let's make this a quadratic equation h^2 + 3h - 28 = 0 (h + 7)(h - 4) h + 7 = 0 OR h - 4 = 0 h = -7 h = 4 Height must be 4 cm because it's impossible to have a negative number as the height. So to find the base you do 4 times two which is 8, then add 6 which is 14cm. Height is 4cm Base is 14cm Check it if you don't believe me... 4 times 14 is 56 56 divided by 2 is 28!!!

Answer 3

Answering 8. first, it is a regular pyramid if V is directly above the intersection of the diagonals.
1. 10 cm
2. indeterminate
3. indeterminate
4. indeterminate
5. indeterminate
6. A = 4(1/2)(6)(8) = 96 cm^2
7. indeterminate
2,3,4,5&7 are indeterminate because the location of V,M,&N are unknown. One could set up inequalities for them, but it is hardly worth the effort.