Estimate the perimeter and the area of the shaded figure to the nearest tenth.

Perimeter: 45.1 units

Area: 401.9 units squared

Step-by-step explanation:

This is fun! I'm honored to help.

We can break this shape down into two formations: a semicircle (also known as a half-circle) and a 2 x 8 rectangle. Calculating the area and the perimeter will be way easier by splitting the figure in two.

The equation for the area of a circle: A = πr^2

The equation for the circumference of a circle: C = 2(πr) or you can think of it as πd, with d being the diameter of the circle.

Make sure to memorize these formulas. They will help a lot later on!

With that in mind, let's calculate the perimeter first! It's important to divide the semicircle in two because we're only dealing with half of it. Only round pi to the hundredth (3.14) and save the estimations at the end. Your answers will be much more accurate if we do so.

2 * (rectangle's sides) + 2 * (circumference of a semicircle)

Perimeter = 2 * (8 + 2) + 2 * (3.14 * 8)/2

=  45.12 units

Don't forget to round at the end, so this will be 45.1 units.

Onto the area, which will be approached in a very similar way! Try to think about this one and use my explanation to check if you caught on! If not, no worries. That's why I wrote each step down for you!

(area of the rectangle) * (area of a half circle)

Area = (2 * 8) * (3.14 * 4^2)/2

=  16 * 25.12

= 401.92 units squared

And then the final stage: rounding! you should get 401.9 units for calculating the area.

All in all, we have 45.1 units when measuring the perimeter of this strange shape and 401.9 units squared when calculating the area. Please comment if this was wrong. I'll appreciate and update it!

Good luck and keep up the hard work! Thanks for reaching out.

∠cbe and ∠deb are same-side interior angles.

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