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2 years ago

Please help me with the problem below.

Mathematics

2 answers:

xxTIMURxx [149]2 years ago

3 0

Answer:

67.5 cm^2

Step-by-step explanation:

we know the length and width of the rectangle and the triangle in the compound shape.

The area of the rectangle is 10 times 5 = 50

the area of the triangle is

17-10 = 7

7 times 5 is 35

35/2 = 17.5

50 plus 17.5 = 67.5 cm^2

IrinaK [193]2 years ago

3 0

Answer: 67.5

Step-by-step explanation: Since this is a irregular shape, you have to split the two shapes. The rectangles area is 50, and the triangles is 17.5.

To find the area of a triangle multiply 1/2 × base × height

To find the area of a rectangle multiply base × height

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Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.

disa [49]

Answer:

Perimeter = 32.44 units

Area = 30 square units

Step-by-step explanation:

Given

Vertices

A(2,8), B(16,2) and C(6,2)

WE have to determine the lengths of all sides before finding the perimeter and area.

The formula of modulus is:

$d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\$

So the perimeter is:

$Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units$

Using hero's formula,

$s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units$