Question

Help please with this question

Answer 1

Answers
perimeter = 26 units
Area = 22 square units

Step by step

The perimeter is found by adding up all the sides. This polygon has many sides. See the attachment for help how to add the sides and find the unknown side lengths.

If you add the horizontal lengths of 4 + 1 + 4 = 9, the base will equal 9 also.

If you add the vertical lengths of 1 + 1 + 2 = 4, the unknown vertical side will also equal 4.

9 + 9 + 4 + 4 = 26 units perimeter

Area is found by multiplying length x width. For area, I broke the figure into three rectangular shapes to find equal sides for multiplying.
The three shapes are
4x4 = 16
2 x 1 = 2
4 x 1 = 4
________
Total area is 22 square units

Problem solved!

Answer 2

• perimeter: 26 units
• area: 22 square units

Explanation:

You want the perimeter and area of the given composite figure.

Perimeter

You will notice that the sum of vertical lengths on the right side of the figure has the same total as the vertical length on the left side:

2 + 1 + 1 = 4 . . . . units high

Likewise, the horizontal lengths at the top of the figure have the same total as the horizontal length at the bottom:

4 + 1 + 4 = 9 . . . . units wide

The perimeter is the sum of all side lengths, so is ...

P = 2(L+W) = 2(9 +4) = 26

The perimeter of the polygon is 26 units.

Composition

The blue lines in the attachment show the area can be divided into rectangles whose area is easily computed. The top rectangle has a width of 4 units and a height of 2 units, so its area is ...

A = WH = (4)(2) = 8 . . . . square units

The middle rectangle has a width of 5 units and a height of 1 unit, so its area is ...

A = WH = (5)(1) = 5 . . . . square units

The bottom rectangle has a width of 9 units and a height of 1 unit, so its area is ...

A = WH = (9)(1) = 9 . . . . square units

Area

The total area of the polygon is the sum of the areas of its parts:

area = top rectangle + middle rectangle + bottom rectangle

= (8 + 5 + 9) square units = 22 square units

The area of the polygon is 22 square units.