Q14b how to find total area of shaded parts?

# STUCK ON HOMEWORK?

## ASK FOR HELP FROM OUR KIASUPARENTS.COM COMMUNITY!

# Question

# Answer

Area of rectangle -> B × L = BL

Area of unshaded triangle 2 -> ½ × B × L = ½BL

Area of shaded parts -> area of rectangle – area of unshaded triangle 2 = BL – ½BL = ½BL

Alternatively

Area of triangle 1 -> ½ × B × L_{1} = ½BL_{1}

Area of triangle 3 -> ½ × B × L_{2} = ½BL_{2}

Area of shaded parts -> ½BL_{1} + ½BL_{2} = ½B(L_{1} + L_{2})

But since L_{1} + L_{2} = L, area of shaded parts -> ½BL

½BL is half of the rectangle

Area of rectangle -> B × L = BL

Area of unshaded triangle 2 -> ½ × B × L = ½BL

Area of shaded parts -> area of rectangle – area of unshaded triangle 2 = BL – ½BL = ½BL

Alternatively

Area of triangle 1 -> ½ × B × L_{1} = ½BL_{1}

Area of triangle 3 -> ½ × B × L_{2} = ½BL_{2}

Area of shaded parts -> ½BL_{1} + ½BL_{2} = ½B(L_{1} + L_{2})

But since L_{1} + L_{2} = L, area of shaded parts -> ½BL

½BL is half of the rectangle

Thank you for explaining so clearly the triangle in rectangle concept.

(a)

area of triangle ABQ = (1/2) x (5 + 5) x 5 = 25 sq cm

(b)

area of triangle BPQ = area of triangle ABQ = 25 sq cm

area of BCQ = (1/2) x 10 x 5 = 25 sq cm

total area of shaded part = 25 + 25 + [(1/2) x 3.14 x 5 x 5 – 25] = 64.25 sq cm

Ans : (a) 25 sq cm; (b) 64.25 sq cm.

Oh, I just realised that half of the rectangle is also shaded.

Area of triangle PBQ = 0.5 × 10 × 5 = 25

Area of triangle BCQ = Area of triangle ABQ = 25

Area of triangle PCQ = 25 + 25 = 50

Total area of the shaded parts = 14.25 + 50 = 64.25 cm²

Hi THW,

Answer is correct, but I do not understand why the shaded part of the rectangle is considered half of the rectangle?

Area of rectangle -> B × L = BL

Area of unshaded triangle 2 -> ½ × B × L = ½BL

Area of shaded parts -> area of rectangle – area of unshaded triangle 2 = BL – ½BL = ½BL

Alternatively

Area of triangle 1 -> ½ × B × L_{1} = ½BL_{1}

Area of triangle 3 -> ½ × B × L_{2} = ½BL_{2}

Area of shaded parts -> ½BL_{1} + ½BL_{2} = ½B(L_{1} + L_{2})

But since L_{1} + L_{2} = L, area of shaded parts -> ½BL

½BL is half of the rectangle

Area of rectangle -> B × L = BL

Area of unshaded triangle 2 -> ½ × B × L = ½BL

Area of shaded parts -> area of rectangle – area of unshaded triangle 2 = BL – ½BL = ½BL

Alternatively

Area of triangle 1 -> ½ × B × L_{1} = ½BL_{1}

Area of triangle 3 -> ½ × B × L_{2} = ½BL_{2}

Area of shaded parts -> ½BL_{1} + ½BL_{2} = ½B(L_{1} + L_{2})

But since L_{1} + L_{2} = L, area of shaded parts -> ½BL

½BL is half of the rectangle

Thank you for explaining so clearly the triangle in rectangle concept.

(a) Area of triangle ABQ = 0.5 × 10 × 5 = 25

(b) Area of square ABCQ = 25 × 2 = 50

Area of circle – area of square ABCQ = 3.14 × 5² – 50 = 28.5

Area of shaded part = 28.5 ÷ 2 = 14.25 cm²

**Find Tuition/Enrichment Centres**