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2 years ago

The figure is made up of 2 rectangles and 2 right triangles

Mathematics

1 answer:

Lemur [1.5K]2 years ago

7 0

Answer:

total area = 132 units²

Step-by-step explanation:

Area of a rectangle = width x height
Area of a triangle = 1/2 x base x height

Area of largest rectangle = 4 x 15 = 60 units²

Area of smallest rectangle = 4 x 6 = 24 units²

Area of largest triangle = 1/2 x (15 - 6) x (4 + 4) = 36 units²

Area of smallest triangle = 1/2 x 6 x 4 = 12 units²

Total area of the figure = sum of areas of 2 rectangles and 2 triangles

⇒ area = 60 + 24 + 36 + 12 = 132 units²

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What is the area of this triangle ?

oee [108]

Answer:

Area of triangle is 9.88 units^2

Step-by-step explanation:

We need to find the area of triangle

Given E(5,1), F(0,4), D(0,8)

We will use formula:

$Area\,\,of\,\,triangle =\sqrt{s(s-a)(s-b)s-c)} \\where\,\, s = \frac{a+b+c}{2}$

We need to find the lengths of side DE, EF and FD

Length of side DE = a = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side DE = a = $=\sqrt{(5-0)^2+(1-8)^2}\\=\sqrt{(5)^2+(-7)^2}\\=\sqrt{25+49}\\=\sqrt{74}\\=8.60$

Length of side EF = b = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side EF = b = $=\sqrt{(0-5)^2+(4-1)^2}\\=\sqrt{(-5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}\\=5.8$

Length of side FD = c = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Length of side FD = c = $=\sqrt{(0-0)^2+(8-4)^2}\\=\sqrt{(0)^2+(4)^2}\\=\sqrt{0+16}\\=\sqrt{16}\\=4$

so, a= 8.60, b= 5.8 and c = 4

s = a+b+c/2

s= 8.6+5.8+4/2

s= 9.2

Area of triangle= $=\sqrt{s(s-a)(s-b)s-c)}\\=\sqrt{9.2(9.2-8.6)(9.2-5.8)(9.2-4)}\\=\sqrt{9.2(0.6)(3.4)(5.2)}\\=\sqrt{97.5936}\\=9.88$

So, area of triangle is 9.88 units^2

4 0

3 years ago

A skier needs to buy new ski poles during a ski trip to utah . The price of the poles is $24 and the sales tax is 4.7%. What is

leva [86]

$total\ cost=\ price\ of\ poles+sales\ tax\\\\
total\ cost=24+4.7\%*24=24+0.047*24=24+1,128\\\\=25.128\approx25.13\$\\\\
Total\ cost\ is\25 .13\$.$

6 0

3 years ago

Veda solves the following system of linear equations by eliminations. What is the vale of x in the solution of the system of equ

kupik [55]

Answer:

x = -1, y = 1

Step-by-step explanation:

6 + 4x - 2y = 0 (1)

-3 - 7y = 10x (2)

From (1)

6 + 4x - 2y = 0 (1)

4x - 2y = -6 (3)

From (2)

-3 - 7y = 10x (2)

10x + 7y = -3 (4)

4x - 2y = -6 (3)

10x + 7y = -3 (4)

Using elimination method

Multiply (3) by 10 and (4) by 4 to eliminate x

40x - 20y = -60

40x + 28y = -12

28y - (-20y) = -12 - (-60)

28y + 20y = -12 + 60

48y = 48

y = 48/48

y = 1

Substitute y = 1 into (3)

4x - 2y = -6 (3)

4x - 2(1) = -6

4x - 2 = -6

4x = -6 + 2

4x = -4

x = -4/4

x = -1

x = -1, y = 1

The value of x in the equation is -1

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3 years ago

The area of a square is given by and the perimeter is given by , where s is the side length of the square. If the side length of

Thepotemich [5.8K]

The area of a square is always:

A=s^2 where s=side length, in this case:

A=4^2=16 in^2

The perimeter of a square is always:

P=4s, in this case:

P=4*4=16 in

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3 years ago

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BARSIC [14]

Answer: C.

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2 years ago

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