Answer:
[tex]\textsf{Area of } \boxed{\quad} = \boxed{\quad 135 \quad } \; \sf in^2 [/tex]
[tex]\textsf{Area of } \triangle = \boxed{\quad 120 \quad } \sf \; in^2 [/tex]
[tex]\textsf{Area of Figure } = \boxed{\quad 255 \quad } \sf \; in^2 [/tex]
Step-by-step explanation:
To find the total area of the figure comprising a rectangle and a triangle, we need to calculate the areas of each shape separately and then add them together.
Given:
Rectangle:
- Base (b) = 15 in
- Height (h) = 9 in
Triangle:
- Base (b) = 16 in
- Height (h) = 15 in
Area of Rectangle:
[tex] \textsf{Area} = b \times h \\\\ = 15 \times 9 \\\\ = 135 \textsf{in} ^2 [/tex]
Area of Triangle:
[tex] \textsf{Area} = \dfrac{1}{2} \times b \times h \\\\ = \dfrac{1}{2} \times 16 \times 15 \\\\ = 120 \textsf{in}^2 [/tex]
Total Area of Figure:
[tex] \textsf{Total Area} = \textsf{Area of Rectangle} + \textsf{Area of Triangle} \\\\ = 135 + 120 \\\\ = 255 \textsf{in} ^2[/tex]
So, the total area of the figure (rectangle and triangle combined) is 255 in².
