Question 1 of 25

Here is a triangular pyramid and its net.

bazaltina [42]

Answer:

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

${\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}$

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

$\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}$

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to Lateral Surface Area + Area of base

$\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}$

Hence,

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

3 0

3 years ago

Find the volume of the solid under the plane 5x + 9y − z = 0 and above the region bounded by y = x and y = x4.

svp [43]

For the plane, we have z = 5x + 9y

For the region, we first find its boundary curves' points of intersection.
x = x^4 ==> x = 0, 1.

Since x > x^4 for y in [0, 1],

The volume of the solid equals

$\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx \\ \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx \\ \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\ \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0$

$=\frac{19}{6} - \frac{5}{6} - \frac{1}{2} =\bold{ \frac{11}{6} \ cubic \ units}$

8 0

2 years ago

Por qué la triangulación con dos diagonales en un rectángulo no es adecuada para calcular el

kherson [118]

Answer:

rfgcc ft v crytrcvrcvhtfvyrfftv ffg

Step-by-step explanation:

tgfgghcg gn v v

4 0

2 years ago

Graph the system of

9966 [12]

Answer:

(-0.2, 2.8)

General Formulas and Concepts:

Algebra I

Reading a Cartesian plane
Coordinates (x, y)
Solving systems of equations by graphing

Step-by-step explanation:

Where the 2 lines intersect is the solution to the systems of equations.

6 0

2 years ago

Plz help me on dis math

vlabodo [156]

The first answer is B: 2 1/2

4 5/6 is put there twice except the last one is subtracting so you can put, 4 5/6 - 4 5/6 = 0 therefore the only number left is 2 1/2

the second one I really don't know sorry:(

The third answer is C because the cases come in 24. But they didn't tell you how many case she brought so the variable has to be by 24 and they took 43 which is the subtracting factor. So the answer is C.

And I also don't know the last one again sorry:(

8 0

3 years ago