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Dmitry [639]
3 years ago
7

What is the area of this composite shape? Enter your answer in the box. _in²

Mathematics
1 answer:
LuckyWell [14K]3 years ago
3 0

The area of the composite figure is 40 in^2

Explanation:

From the given figure, we can see that the area of the composite figure = area of the rectangle + area of the triangle.

Area of the rectangle (A_1):

The formula is given by

A_1=length\times width

where length = 5 and width = 5

Substituting, we have,

A_1=7\times 5=35 in^{2}

Thus, the area of the rectangle = 35 i n^{2}

Area of the triangle (A_2):

The formula is given by

A_2=\frac{1}{2} bh

where b=5-3=2 i n

and h=12-7=5 \text { in }

Substituting, we have,

A_2=\frac{1}{2} (2)(5)\\A_2=5 in ^{2}

Thus, the area of the triangle = 5in ^{2}

Area of the composite figure = Area of the rectangle + area of the triangle

Area of the composite figure = 35 i n^{2}+5 i n^{2}=40 i n^{2}

Thus, the area of the composite figure is 40 in^2

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Dimensions: A=a\cdot b=256

Perimiter: P=2a+2b

Minimum perimeter: [16,16]

Step-by-step explanation:

This is a problem of optimization with constraints.

We can define the rectangle with two sides of size "a" and two sides of size "b".

The area of the rectangle can be defined then as:

A=a\cdot b=256

This is the constraint.

To simplify and as we have only one constraint and two variables, we can express a in function of b as:

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We can express the diameter as:

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To optimize we can derive the function and equal to zero.

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The minimum perimiter happens when both sides are of size 16 (a square).

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