376,786 views
8 votes
8 votes
Simple Composite figures question. Find the area of the shape.

Simple Composite figures question. Find the area of the shape.-example-1
User Yiu
by
3.1k points

1 Answer

22 votes
22 votes

9514 1404 393

Answer:

453.9 m²

Explanation:

It considerably simplifies the area calculation to assume the figure decomposes to a parallelogram and an equilateral triangle.

The area of the parallelogram is ...

A = bh

A = (17 m)(6 m) = 102 m²

The area of the equilateral triangle—using the given altitude—is ...

A = 1/2bh

A = 1/2(17 m)(14.7 m) = 124.95 m²

The area of the whole figure is double the sum of these areas, so is ...

A = 2(102 m² +124.95 m²) = 453.9 m²

The area of the shape is 453.9 m².

__

Additional comment

Unless we make some assumptions about the location of the concave exterior angle at the left and right, we cannot compute the area of the figure. At least, we must assume the 10 m segments are parallel. If that is the only assumption, and other dimensions are taken at face value, the area of the figure computes to about 453.4 m². As you can see from the attachments, the altitude of 14.7 is not quite enough to make the triangle equilateral. That prevents the quadrilateral from being a parallelogram.

Further dividing the quadrilateral along its short diagonal, various lengths and angles can be found using the law of sines and the law of cosines. Then the figure area can be found as the sum of triangle areas: two triangles in the quadrilateral, and the one with altitude 14.7. This alternate approach is shown in the second attachment.

Simple Composite figures question. Find the area of the shape.-example-1
Simple Composite figures question. Find the area of the shape.-example-2
User Muhammad Ahmod
by
2.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.