We read your photo as:

Find the area of the below shape. (π=22/7)

Mathematics

ScanSolve AI Answer

Step-by-step solution

9 steps

:
The first shape is a triangle with a given base and height.

  1. Identify the formula for the area of a triangle.

    The area of a triangle (AA) is calculated using the formula:

    A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

  2. Substitute the given values into the formula.

    From the image, the base (bb) is 5 cm and the height (hh) is 17 cm.

    A=12×5 cm×17 cmA = \frac{1}{2} \times 5 \text{ cm} \times 17 \text{ cm}

  3. Calculate the area.

    A=12×85 cm2A = \frac{1}{2} \times 85 \text{ cm}^2 A=42.5 cm2A = 42.5 \text{ cm}^2

    The area of the triangle is 42.5 cm2\boxed{\text{42.5 cm}^2}.

    :
    The second shape consists of two concentric circles, and we need to find the area of the region between them (an annulus). We are given the diameters and instructed to use π=227\pi = \frac{22}{7}.

  4. Determine the radii of the outer and inner circles.

    The radius is half of the diameter.
    Outer radius (RR) = 56 cm2=28 cm\frac{56 \text{ cm}}{2} = 28 \text{ cm}
    Inner radius (rr) = 5 cm2=2.5 cm\frac{5 \text{ cm}}{2} = 2.5 \text{ cm}

  5. Identify the formula for the area of an annulus.

    The area of an annulus (AA) is the difference between the area of the outer circle and the area of the inner circle:

    A=πR2−πr2=π(R2−r2)A = \pi R^2 - \pi r^2 = \pi (R^2 - r^2)

  6. Substitute the values into the formula.

    A=227((28 cm)2−(2.5 cm)2)A = \frac{22}{7} ((28 \text{ cm})^2 - (2.5 \text{ cm})^2)

  7. Calculate the squares of the radii.

    R2=(28)2=784 cm2R^2 = (28)^2 = 784 \text{ cm}^2 r2=(2.5)2=6.25 cm2r^2 = (2.5)^2 = 6.25 \text{ cm}^2

  8. Substitute the squared values and calculate the difference.

    A=227(784 cm2−6.25 cm2)A = \frac{22}{7} (784 \text{ cm}^2 - 6.25 \text{ cm}^2) A=227(777.75 cm2)A = \frac{22}{7} (777.75 \text{ cm}^2)

  9. Perform the final multiplication and division.

    A=22×777.757 cm2A = \frac{22 \times 777.75}{7} \text{ cm}^2 A=17110.57 cm2A = \frac{17110.5}{7} \text{ cm}^2 A≈2444.36 cm2A \approx 2444.36 \text{ cm}^2

    The area of the shape is 2444.36 cm2\boxed{\text{2444.36 cm}^2}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QFind the area of the shape below. TAKE pi = 22/7QFind the area (π = 22/7)QUsing pi = 22/7, find the area of the shaded region.QFind the area of the following shape. Use Use pi=3.142 and give your answer correct to 1 decimal…QFind the area of a semi-circle whose radius is 7cm. [Take π = 22/7]
Browse by topic:Geometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp