1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lbvjy [14]
11 months ago
8

1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an

apothem SM = √15 cm. Calculate the pyramid: 1) the base elevation AM; 2) the elevation SO; 3) the area of the base; 4) the area of the side surface; 5) the total surface area; 6) volume.

Mathematics
1 answer:
Musya8 [376]11 months ago
7 0

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

\begin{gathered} AM=\sqrt{AB^2-BM^2} \\  \\ AM=\sqrt{6^2-3^2} \\  \\ AM=\sqrt{36-9} \\  \\ AM=\sqrt{27} \\  \\ AM=5.2\text{ cm} \end{gathered}

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

SO=\sqrt{SM^2-MO^2}

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\  \\ SO=\sqrt{15-6.76} \\  \\ SO=2.9\text{ cm} \end{gathered}

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

A=\frac{1}{2}*BC*AM

Thus, we have:

\begin{gathered} A=\frac{1}{2}*6^*5.2 \\  \\ A=15.6\text{ cm}^2 \end{gathered}

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

SA=\frac{1}{2}*p*h

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\  \\ A=34.86\text{ cm}^2 \end{gathered}

• (5). Total surface area:

To find the total surface area, apply the formula:

TSA=base\text{ area + area of side surface}

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

V=\frac{1}{3}*area\text{ of base *height}

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\  \\ V=15.08\text{ cm}^3 \end{gathered}

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

You might be interested in
An isosceles triangle ABC with the base BC is inscribed into a circle. Find the measure of angles of it, if measure of arc BC=10
zzz [600]

Answer:

The measures of the angles of ΔABC are

m∠A = 51° , m∠B = 64.5 , m∠C = 64.5°

Step-by-step explanation:

* Lets revise some facts in the circle

- The measure of the circle is 360°

- Equal chords intercept equal arcs

- The measure of an inscribed angle equals half the measure

 of the intercepted arc

* Lets solve the problem

- ΔABC is isosceles withe base BC

∴ AB = AC

- The vertex angle is A

∵ ∠A is an inscribed angle subtended by arc BC

∴ m∠A = 1/2 the measure of arc BC

∵ The measure of arc BC = 102° ⇒ given

∴ m∠A = 1/2(102) = 51°

- In ΔABC

∵ AB = AC ⇒ proved

∴ m∠B = m∠C ⇒ base angles of isosceles Δ

- The sum of the interior angles in any Δ = 180°

∵ m∠A = 51 ⇒ proved

∴ m∠B = m∠C = (180 - 51) ÷ 2 = 129 ÷ 2 = 64.5°

* The measures of the angles of ΔABC are

  m∠A = 51° , m∠B = 64.5° , m∠C = 64.5°

5 0
3 years ago
Read 2 more answers
Which expression has the greater value? Justify your answer. −8 + 3 −8 × 3
barxatty [35]
Did u mean -8+3= and -8x3= cuz if so then it’s -8+3=-5 and -8x3=-24 so it would be -8+3
8 0
3 years ago
Is 99.01 greater than 99.10
fiasKO [112]

No, .01 is farther from being 1 than .1 is.

5 0
3 years ago
Read 2 more answers
I need an explantion on this question
svlad2 [7]
Y= -x + 2 and y= 3x - 4
As these both equal y, you know that they both equal each other so
-x + 2 = 3x - 4
Third option :)
5 0
2 years ago
Read 2 more answers
Amber's bank statement shows a closing balance of $224.13. There are no outstanding checks deposits. Her checkbook shows a balan
Lina20 [59]
Interest earned in the amount of $2.75
4 0
3 years ago
Read 2 more answers
Other questions:
  • How do you do it to find the answer
    15·1 answer
  • a city block is a square with each side measuring 102 yards. Find the length of the diagonal of the city block.
    15·1 answer
  • What does 4/x+5 + 2x/x^2-25 equal?
    11·1 answer
  • State whether the following are describing distance (d), velocity (v), or acceleration (a)
    10·1 answer
  • What is 45 1/2% as a fraction in simplest form?
    11·1 answer
  • What is 78.9 in word form?
    9·2 answers
  • How do we find an equation of a linear function by giving two<br> points
    6·1 answer
  • Find the GCF of the equation 18x^3 +3x^2-6x
    8·1 answer
  • ANSWER !! <br> ILL GIVE 40 POINTS !!<br> DONT SKIP :(( <br> PLUS BRAINLIEST !
    12·1 answer
  • Find the total surface area of this cone
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!