Question

Find the area of the shaded polygons.
(Im giving 100 points to whoever solves)

Answer 1

see below

Explanation:

To find:-

• The areas of the given shaded polygons.

Answer:-

There are three polygons viz parallelogram, triangle and a trapezium. To find out the areas we can use the following formulae :-

Area of triangle :-

• Area = 1/2 * base * height

Area of parallelogram:-

• Area = base * perpendicular height

Area of trapezium:-

• Area = 1/2 * (sum of parallel sides)*distance between the sides

Now we may use the above formulae as ,

Area of the given parallelogram:-

→ A = base * height

→ A = * 15 * 8

→ A = 120units²

Area of the given triangle:-

→ A = 1/2 * b * h

→ A = 1/2 * 5 * 7

→ A = 17.5 units²

Area of the given trapezium:-

→ A = 1/2 * sum of || sides* distance between them

→ A = 1/2 * (7+24) * 24

→ A = 12 * 31

→ A = 372 units ²

This is our required answers .

Answer 2

Area of the parallelogram = 120 square units

Area of the triangle = 17.5 square units

Area of the trapezoid = 372 square units

Explanation:

The first polygon is a parallelogram with a base of 15 units and a height of 8 units.

`\begin{aligned}\sf Area\;of\;a\;parallelogram&=\sf base * height\\&=\sf 15 * 8\\&=\sf 120\;square\;units\end{aligned}`

Therefore, the area of the parallelogram is 120 square units.

`\hrulefill`

The second polygon is a triangle with a base of 5 units and a height of 7 units.

`\begin{aligned}\sf Area\;of\;a\;triangle&=\sf (1)/(2) * base * height\\\\&=\sf (1)/(2) * 5 * 7\\\\&=\sf 17.5\;square\;units\end{aligned}`

Therefore, the area of the triangle is 17.5 square units.

`\hrulefill`

The third polygon is a trapezoid with bases of 7 units and 24 units, and a height of 24 units.

`\begin{aligned}\sf Area\;of\;a\;trapezoid&=\sf (sum\;of\;bases)/(2) * height\\\\&=\sf (7+24)/(2) * 24\\\\&=\sf (31)/(2)* 24\\\\&=\sf 372\;square\;units\end{aligned}`

Therefore, the area of the trapezoid is 372 square units.