Honors Geometry QUiz- Please Help

QUESTION 2:
What is the area of this polygon?





28.5 units²

34.5 units²

37.5 units²

40.5 units²
------------------------

QUESTION 3:

The curved part of this figure is a semicircle.

What is the best approximation for the area of this figure?


24+9.125π units²

12+9.125π units²

24+18.25π units²

12+18.25π units²
_______________

QUESTION 4:

This figure is made up of a rectangle and parallelogram.

What is the area of this figure?



Enter your answer in the box. Do not round any side lengths.

?units²
_____________


QUESTION 5

What is the area of this composite shape?


Enter your answer in the box.

?in²

pLEASE gIVE vAILD eXPLINATION

Answer:

QUESTION 2:

The area of the polygon is 21.5 units²

QUESTION 3:

The area of the combined figure is 12 + 18.25·π units²

QUESTION 4:

The area of the figure is 40 units²

QUESTION 5

The area of the compost shape is 40 in.²

Step-by-step explanation:

QUESTION 2.

The area of the polygon is given as follows;

The area of two triangles + The area of trapezoid

1/2×6×3 + 1/2×3×4 + 1/2×(6 + 7) = 21.5 units²

QUESTION 3

The diameter of the semicircle, 'd', is given as follows;

d = √(8² + 3²) = √73

The area of the semicircle = π·d²/4 = π·73/4 = 18.25·π unit²

The area of the right triangle beside the semicircle is given as follows;

1/2 × 8 × 3 = 12 unit²

The area of the combined figure = The area of the semicircle + The area of the right triangle

∴ The area of the combined figure = 12 + 18.25·π units²

QUESTION 4:

The dimensions of the parallelogram are;

Width, W = √(4² + 1²) = √(17)

Length, L = √(8² + 2²) = √(68)

The area of the parallelogram, [tex]A_R[/tex] = W × L = √(17) × √(68) = √(17 × 68) = 34

The area of the parallelogram, [tex]A_R[/tex] = 34 units²

The length of a parallel side, 'A', of the parallelogram is A = 6

The height of the parallelogram, is h = 1

The area of the parallelogram is A = B·h = 6 × 1 = 6 units²

The area of the figure is the sum of the area of the rectangle and the area of the parallelogram

Therefore, we have;

The area of the figure = 34 units² + 6 units² = 40 units²

QUESTION 5

The composite shape consists of a triangle and a rectangle

Therefore, we have;

The area of the rectangle = 5 in. × 7 in. = 35 in.²

The area of the triangle = 1/2 × 2 in. × 5 in. = 5 in.²

The area of the compost shape = The area of the rectangle + The area of the triangle

∴ The area of the compost shape = 35 in.² + 5 in.² = 40 in.²

The area of the compost shape = 40 in.².

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