Given:
LM
||
KN
,
KL
||
NM
,
LP = h1 = 5 cm, MQ = h2 = 6 cm,
PKLMN = 42 cm
Find: Area of KLMN.
To find the area of KLMN, we can break it down into smaller shapes and then calculate their areas.
1. Find the area of triangle KLP:
Since LP is given as 5 cm and the height h1 is given as 5 cm, we can use the formula for the area of a triangle: Area = (base * height) / 2.
Area of triangle KLP = (5 * 5) / 2 = 25 / 2 = 12.5 cm².
2. Find the area of triangle KMN:
Since MN is given as 6 cm and the height h2 is given as 6 cm, we can use the formula for the area of a triangle: Area = (base * height) / 2.
Area of triangle KMN = (6 * 6) / 2 = 36 / 2 = 18 cm².
3. Find the area of rectangle KLMN:
The area of a rectangle is calculated by multiplying its length and width.
Since KL is the common side of both triangles, we can use its length as the length of the rectangle.
KL = LP + PN = 5 cm + 6 cm = 11 cm.
The width of the rectangle is given by the height difference between the two triangles: h2 - h1 = 6 cm - 5 cm = 1 cm.
Area of rectangle KLMN = Length * Width = KL * (h2 - h1) = 11 cm * 1 cm = 11 cm².
4. Find the total area of KLMN:
To get the total area of KLMN, we add the areas of the two triangles and the rectangle.
Total area of KLMN = Area of KLP + Area of KMN + Area of KLMN = 12.5 cm² + 18 cm² + 11 cm² = 41.5 cm².
Therefore, the area of KLMN is 41.5 cm².