Question

Hello, may I please have some help on these 4 questions? Thanks very much! {Also, if you could answer them quick, that would be highly appreciated!}

Answer 1

1.

Parallelogram with base a = 20 in. and height h = 16 in.
Triangle with base a = 20 in. and height b = 8 in.

so:

$A = A_P+A_T=a\cdot h+\frac{1}{2}\cdot a\cdot b=20\cdot16+\frac{1}{2}\cdot20\cdot8=320+80=\\\\=\boxed{400\text{ in}^2}$

2.

Trapezoid with base b₁ = 14 cm, base b₂ = 4 cm and height h = 10 cm
Triangle with base b₁ = 14 cm and height x = 18 cm - 10 cm = 8 cm

so:

$A=A_T+A_\Delta=\frac{1}{2}\cdot(b_1+b_2)\cdot h+\frac{1}{2}\cdot b_1\cdot x=\\\\= \frac{1}{2}\cdot(14+4)\cdot 10+\frac{1}{2}\cdot 14\cdot8=\frac{1}{2}\cdot18\cdot 10+\frac{1}{2}\cdot 14\cdot8=90+56=\\\\=\boxed{146\text{ cm}^2}$

3.

We have three rectangles:

$A=A_1+A_2+A_3=1\cdot 4+6\cdot5+18\cdot6=4+30+108=\boxed{142\text{ ft}^2}$

4.

Area of a circle:

$A_\circ=\pi\cdot r^2=3.14\cdot5^2=3.14\cdot25=78.5 \text{ cm}^2$

Area of a rectangle:

$A_R=8\cdot 6=48\text{ cm}^2$

Area of the shaded region:

$A=A_\circ-A_R=78.5-48=\boxed{30.5\text{ cm}^2}$