area and perimeter of a compound figure

Question

https://ibb.co/RTJjtVdv

Answer 1

Without making a few assumptions, it is not possible to solve this question as it is not very clear (and the figure is not drawn to scale using the squares)

My assumptions are:

1 - The triangle is an equilateral triangle with a side length A = 6.

2 - The 4-sided shape in the middle is a rectangle with width (W) = 6

3 - The curve at the bottom is a semi-circle and 10 corresponds to the diameter (D) of that circle.

4 - The diameter of the semi-circle is exactly half of the longest side of the rectangle.

With the above assumptions, you can move forward as follows:

1 - Long side of the rectangle (L) is 20 since it is equal to 2 x 10

2 - The remaining length of L excluding the base of the triangle (K) is 20 - 6 = 14

3 - The length of the half circle (H) = 1/2 x D x (pi) where pi=3.14. So H = 1/2 x 10 x 3.14 = 15.7

The perimeter of the irregular shape (P) is calculated as follows:

P = (2 x W) + (L - D) + H + K + (2 x A)

By plugging the numbers in, we get:

P = (2 x 6) + (20 - 10) + 15.7 + 14 + (2 x 6) = 63.7

Answer 2

This image is missing some information necessary to make these calculations. We can make some assumptions, but we all know what assuming does! ;) However, here are the assumption I would make if I were to do something so reckless:

1. the triangle on top is isosceles,
2. point where it intersects the rectangle is at the midpoint of the rectangle's base
3. the semi-circle intercepts the rectangle at midpoint of the rectangle's other base

Now the calculations:

1. Circumference of the semi-circle: C=πr, so C=π(2.5)≈7.85
2. Segment distances:
3. 6 + 6 (around the triangle)
4. 5 + 5 (combination of distance across from triangle to edge of rectangle and semi-circle to other edge)
5. 6 + 6 (combination of heights)
6. Full perimeter (adding all that together): 41.85 m

For area, we need to combine the areas of the three figures:

1. Isosceles Triangle A = 1/2 bh.
2. Use Pythagorean Theorem (a²+b²=c²) to find the height:h²+2.5²=6², so h = √29.75≈5.45
3. A = 1/2(5)(5.45) = 13.63 m²
4. The Rectangle A = bh (aka lw) = (10)(6) = 60 m²
5. For Semi-circle A = 1/2πr² = (2.5²)π/2≈9.82 m²
6. Combined area: 83.48 m²

Keep in mind, the whole thing changes if these assumptions are not correct. For example, if that's an equilateral triangle. Please, make sure that any Geometry diagrams have ALL markings.

Answer 3

There's not enough information provided here unless some assumptions are made.

Assumption 1: The middle shape is a rectangle.

Assumption 2: The triangle is isosceles.

Assumption 3: The base of the triangle extends from the left side of the rectangle to the midpoint of the rectangle's upper side.

Assumption 4: The bottom shape is a semicircle.

Assumption 5: The semicircle extends from the right side of the rectangle to the midpoint of the rectangle's lower side.

Based on those assumptions, you can say the base of the triangle is 5 units long and the height can be determined using the Pythagorean Theorem (2.5² + h² = 6² then solve for "h"). You can also say the radius of the semicircle is 2.5 which allows you to calculate the area using A = (1/2)(π)(r²) and the perimeter (half the circumference) using C = (1/2)(2)(π)(r)