In the figure ABCD, it is given that BC || AD. BC= 10cm AD = 6cm , AE = 5cm and is perpendicular to BC . Find the area of the figure ABCD
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In the figure ABCD, it is given that BC || AD. BC= 10cm AD = 6cm , AE = 5cm and is perpendicular to BC . Find the area of the figure ABCD
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Answer:
So, the area of the figure ABCD is 110 square centimeters.
Step-by-step explanation:
To find the area of the figure ABCD, you can use the fact that BC is parallel to AD, and the height of the figure AE is perpendicular to BC. This means that the figure can be divided into two rectangles: ABCD and ABE. To find the area of the entire figure, simply add the areas of these two rectangles.
Area of ABCD:
Since BC is parallel to AD, the length of DC is also 6 cm (equal to AD).
So, the area of ABCD = AD * BC = 6 cm * 10 cm = 60 square cm.
Area of ABE:
The area of a rectangle is given by its length times its width.
In this case, the length of ABE is AE, which is 5 cm, and the width is BC, which is 10 cm.
So, the area of ABE = AE * BC = 5 cm * 10 cm = 50 square cm.
Now, add the areas of both rectangles to find the total area of the figure ABCD:
Total area = Area of ABCD + Area of ABE
Total area = 60 square cm + 50 square cm = 110 square cm.
So, the area of the figure ABCD is 110 square centimeters.