Answer:
a) 92.5 in² (nearest tenth)
b) 260 m²
Step-by-step explanation:
Formulas
[tex]\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}[/tex]
[tex]\textsf{Area of a triangle}=\dfrac12 \times \sf base \times height[/tex]
[tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}[/tex]
Part (a)
This figure comprises:
- an isosceles triangle (with base of 12 in and height of 6 in)
- a semicircle (with radius of 6 in)
Total Area:
= area of triangle + area of semicircle
[tex]\sf = \dfrac{1}{2} \cdot 12 \cdot 6+\dfrac{1}{2} \pi (6)^2[/tex]
[tex]\sf = 36 + 18 \pi[/tex]
[tex]\sf = 92.5 \:\: in^2 \:(nearest\:tenth)[/tex]
Part (b)
This figure comprises:
- an isosceles triangle (with base of 10 m and height of 12 m)
- a rectangle (with width of 10 m and length of 20 m)
Total Area:
= area of triangle + area of rectangle
[tex]\sf = \dfrac{1}{2} \cdot 10 \cdot 12+10 \cdot 20[/tex]
[tex]\sf = 60+200[/tex]
[tex]\sf = 260 \:\: m^2[/tex]
