All categories

3 years ago

Find the area of the shaded region.

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

8 0

Answer:

C. 96 in²

Step-by-step explanation:

24x8=192

1/2 x24x8= 96

192-96=96

You might be interested in

Solve the equation algebraically: 10 1 X= 7 I I need an explanation too

Snowcat [4.5K]

Elaborate please for

3 0

3 years ago

NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.

slava [35]

Answer:

<h3>Question 7</h3>

Lateral Surface Area

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

$\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2$

Total Surface Area

Area of the isosceles triangle:

$\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2$

Total surface area:

$\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)$

Volume

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3>Question 8</h3>

Lateral Surface Area

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

Total Surface Area

Area of a pentagon:

$\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is the side length.

Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

Volume

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

8 0

2 years ago

Solve. −7x = x2 + 12

adelina 88 [10]

Answer:

x = - 4 , x = - 3

Step-by-step explanation:

- 7x = x^2 + 12

Take all terms to one side of equation.

x^2 + 7x + 12 = 0

Find which 2 numbers multiply to give 12 and add to give 7.

a × b = 12

a + b = 7

a = 4

b = 3

Split the middle term using these 2 numbers.

x^2 + 4x + 3x + 12 = 0

Factorise each pair of terms separately.

x ( x + 4 ) + 3 ( x + 4 ) = 0

Bring out common factor of ( x + 4 ) and factorise.

( x + 4 ) ( x + 3 ) = 0

Using the Null factor law, make the expressions in each pair of parentheses equal 0.

x + 4 = 0

x = - 4

AND

x + 3 = 0

x = - 3

THEREFORE:

x = - 4 , x = - 3

5 0

3 years ago

Read 2 more answers

-7 = (-5) - (-12) true or false

klio [65]

Answer:

False

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A boy is 5 years old and his sister is three times as old as he is.

hichkok12 [17]

His sister will be 20, right!

3 0

3 years ago

Read 2 more answers