find the area of the complex figure 31 cm 12 cm 23 cm 23 cm 31 cm 69 cm
The complex figure you described seems to consist of two rectangles put together, so we can first find the area of each rectangle and then add them together to get the total area of the complex figure.
- The first rectangle has dimensions 31 cm × 12 cm, so its area is 31 cm × 12 cm = 372 cm².
- The second rectangle has dimensions 23 cm × 69 cm, so its area is 23 cm × 69 cm = 1587 cm².
To get the total area, we add the areas of the two rectangles:
Total area = 372 cm² + 1587 cm² = 1959 cm².
Therefore, the area of the complex figure is 1959 cm².
To find the area of a complex figure, we need to break it down into simpler shapes and then find the areas of those shapes separately. In this case, the complex figure is made up of several rectangles. Let's find the area of each rectangle and then add them up to get the total area.
Rectangle 1:
Length = 31 cm, Width = 12 cm
Area = Length * Width = 31 cm * 12 cm = 372 cm²
Rectangle 2:
Length = 23 cm, Width = 23 cm
Area = Length * Width = 23 cm * 23 cm = 529 cm²
Rectangle 3:
Length = 31 cm, Width = 69 cm
Area = Length * Width = 31 cm * 69 cm = 2,139 cm²
Now, let's add up the areas of the rectangles to find the total area of the complex figure:
Total Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3
= 372 cm² + 529 cm² + 2,139 cm²
= 3,040 cm²
Therefore, the area of the complex figure is 3,040 cm².
To find the area of a complex figure, we often need to break it down into simpler shapes and then find the area of each individual shape.
Looking at the measurements given, it seems like we have a combination of rectangles and triangles. Let's break it down step-by-step:
1. Start by identifying the different shapes present in the complex figure.
From the measurements provided, we can see that we have two rectangles and a triangle. Let's label them:
- Rectangle A: 31 cm x 12 cm
- Triangle B: 23 cm base and a height of 23 cm
- Rectangle C: 31 cm x 69 cm
2. Calculate the area of each shape.
a) Rectangle A:
To find the area of a rectangle, use the formula: Area = length x width
Area of Rectangle A = 31 cm x 12 cm = 372 cm²
b) Triangle B:
To find the area of a triangle, use the formula: Area = 0.5 x base x height
Area of Triangle B = 0.5 x 23 cm x 23 cm = 264.5 cm²
c) Rectangle C:
Area of Rectangle C = 31 cm x 69 cm = 2,139 cm²
3. Find the total area of the complex figure.
To find the total area, add up the areas of all the individual shapes:
Total Area = Area of Rectangle A + Area of Triangle B + Area of Rectangle C
Total Area = 372 cm² + 264.5 cm² + 2139 cm² = 2775.5 cm²
Therefore, the area of the complex figure is 2775.5 cm².