Answer:
area = 288.62 mm²
Explanation:
To find the area we divide the complex shape into simple shapes whose areas we can find.
There is a rectangle in the center.
There are 2 congruent triangles on the sides.
We have the lengths of 2 perpendicular sides of the triangles, so they are the base and height.
For the rectangle, we only have the width. We need to find the length.
The length of the rectangle is the hypotenuse of the triangles.
We use the Pythagorean theorem to find the length of the hypotenuse of the right triangle. That is the length of the rectangle.
a² + b² = c²
(10.4 mm)² + (15.3 mm)² = c²
c² = 342.25 mm²
c = 18.5 mm
area = area of triangles + area of rectangle
area = 2 × (1/2)bh + LW
area = 2 × (1/2) × 15.3 mm × 10.4 mm + 18.5 mm × 7 mm
area = 159.12 mm² + 129.5 mm²
area = 288.62 mm²