Let's assume the question is to find the area of the shaded region.
7. We have to assume the bottom right angle is right as well.
Consider the white triangle at the bottom; call its left leg x.
Then the big tra pezoid which includes the shaded part has area
(1/2)((14 + x) + 26)(15)
and the bottom right triangle has area
(1/2)x(15)
and white triangle on the right has
(1/2)(26)(15 - 6)
The total area of the shared part is thus
(1/2)((14 + x) + 26)(15) - (1/2)x(15) - (1/2)(26)(15 - 6)
= (1/2)(15)(40 + x - x) - 13(9)
= 183
Answer: 183 sq in
8. That's an annulus, the difference between two circles. The outer one has radius 21/2 m, the inner one radius 21/2 - 3.5.
A = πR²-πr² = π( (21/2)² - (21/2 - 3.5)² ) = π(2(21/2)(3.5) - 3.5²) = 3.5π(21-3.5)=61.25π
Answer: 61.25π sq m
9. That looks like a parallelogram less a right triangle.
The parallelogram has area 15(23.8)
The right triangle missing leg x satisfies
x² + 21² = 23.8²
x = 11.2
The right triangle area is
(1/2) (21)(11.2)
So the shaded area is
15(23.8) - (1/2) (21)(11.2) =239.4
Answer: 239.4 sq ft
10. That's a circle less a square. The diagonal of the square is 8√2 and the radius of the square is half of that, 4√2
The area is
π(4√2)² - 8² = 32 π - 64
Answer: 32π - 64 sq cm
