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3 years ago

15

A square pyramid has a base of 6 inches. The height of each triangle face is 11 inches. Which expression correctly calculate the

surface area of the pyramid

1 answer:

stira [4]3 years ago

6 0

Step-by-step explanation:

see the image for explanation.

please ask if something not clear.

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A triangle has three sides 35cm 54 cm and 61 cm find its area Also find the smallest of its altitude

I am Lyosha [343]

Answer:

Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

We are given three sides of a triangle, Let the sides be :

( a ) = 35 cm

( b ) = 54 cm

( c ) = 61 cm

We can find the area of the triangle with its three sides using Heron's Formula

<u>Heron's </u><u>Formula</u>

Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

$\sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}$

where ( s ) :

$\sf \longrightarrow s = \dfrac{a + b + c}{2}$

Therefore, for the given triangle first we will calculate ( s )

$\begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}$

Now, Area of triangle will be:

$\begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}$

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

$\begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}$

3 0

2 years ago

Read 2 more answers

School A and B are competing in an academic contest. at the beginning of the final round, school A has 174 points and school B h

7nadin3 [17]

X = number of correct answers

Y = number of incorrect answers

School A has 174 points and school B has 102 points.

A = 174

B = 102

School A has the same number of correct and incorrect answers during the final round.

A = 174 + 10X - 6Y

School B gives no incorrect answers and the same number of correct answers as school A.

B = 102 + 10X

The contest ends with the two schools tied.

Score = 174 + 10X - 6Y = 102 + 10X

174 + 10X - 6Y = 102 + 10X

5 0

3 years ago

17x2 - 5x + 10x - 8x2

USPshnik [31]

Answer:

9x2+5x

Step-by-step explanation:

combine like terms

4 0

3 years ago

In your computation, approximate its value as 3.14.

andrey2020 [161]

Answer: d

Step-by-step explanation:

Find the area of the rectangle.

$A=l*w\\A=(15in)(12in)\\A=180in^2$

Find the area of the base of the semicircle.

$A=\pi r^2$

12 in would be the diameter, divide by 2 to get the radius.

$\frac{12}{2}=6$

Plug this into the formula.

$A=(3.14)(6)^2\\A=113.04in^2$

Since we do not have a full circle but a semi one instead, we must divide our result by 2.

$\frac{113.04}{2}=56.52in^2$

Add both areas.

180+56.52=236.52 $in^2$

7 0

3 years ago

What expression represents a number one fourth as great as 10-2

Bad White [126]

Answer:

8+1/4

Step-by-step explanation:

8+1/4 because 10-2 is 8.

6 0

3 years ago

Read 2 more answers