Question

ABCD is a rectangle, with M the midpoint or BC and N the midpoint of CD. If CM=4 and NC=5, what percent of the area of the rectangle is shaded

Answer 1

87.5%

Explanation:

Given:

• ⇒ ABCD is a rectangle, with M the midpoint of BC and N the midpoint of CD.
• ⇒ CM = 4 and NC = 5.

Area of triangle NCM

⇒ 1/2 × base × height

⇒ 1/2 × CN × CM

⇒ 1/2 × 5 × 4

⇒ 10cm²

Length of rectangle ⇒ 10

Breadth of the rectangle ⇒ 8

↓

Area of rectangle ⇒ Length × Breadth

Area of rectangle ⇒ 10 × 8 = 80cm²

Area of shaded region ⇒ Area of rectangle - Area of triangle

Area of shaded region ⇒ 80 - 10 = 80cm²

Percentage of the shaded region = Shaded/complete rectangle × 100

⇒ 70/80 × 100 = 87.5

⇒ The percent of the area of the rectangle shaded is therefore 87.5%.