The area of the figure in the image is 23.5in²
Triangle and Rectangle
A triangle is simply a polygon with three vertices and three edges.
Area of a right angled triangle is expressed as;
AreaT = 1/2 × base × height
AreaT = 1/2 × b × h
A rectangle is simply a quadrilateral with four right angles.
Area of a rectangle is expressed as;
AreaR = length × width
AreaR = l × w
Given the data in the question;
In the image, there is a small rectangle inside the larger triangle.
Hence,
- Base of the right angled triangle b = 2in + 5in = 7in
- Height of the right angled triangle h = 5in + 4in = 9in
Also
- Length of the rectangle l = 4in
- Width of the rectangle w = 2in
First we calculate the area of the right angled triangle.
AreaT = 1/2 × b × h
AreaT = 1/2 × 7in × 9in
AreaT = 31.5in²
Next we calculate the area of the rectangle.
AreaR = l × w
AreaR = 4in × 2in
AreaR = 8in²
Now, the area of the figure will be;
Area of the right angled triangle - Area of the rectangle
Area of figure = 31.5in² - 8in²
Area of figure = 23.5in²
Therefore, the area of the figure in the image is 23.5in²
Learn more about area of triangle here: brainly.com/question/19305981
