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Alchen [17]
1 year ago
6

10 POINTS ALL FOR YOU IF YOU ANSWER IT

Mathematics
1 answer:
Gennadij [26K]1 year ago
3 0

Answer:

x is equal to 30

<ABC is equal to 100°

<DBC is equal to 80°

Step-by-step explanation:

3x +10 +2x +20 =180

5x = 180 - 10- 20

5x = 150, divide both sides by 5

x is equal to 30

<ABC = 3x + 10 = 3 × 30 + 10 = 100°

<DBC = 180 - <ABC = 180 - 100 = 80°

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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
Musya8 [376]

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.

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Find the length of side x in simplest radical form with a rational a<br> denominator.
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Step-by-step explanation:

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Answer:

35%

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Answer:

A=360in^2

Step-by-step explanation:

there are 5 faces, 2 triangular, 3 rectangular

Triangular:

A=(9 * 10)/2=45

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Rectangular:

A=10*9=90

Since there are 3 the total is 270in^2

Total surface area is A=270+90=360in^2

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