**Area: Composite Shape**

** Q1 **∆ABD and ∆BCD are right angle triangles as shown in the figure. AB is parallel to CD

Find area of the triangle ∆ABC

**Solution**

**Q2 : Application**

Find area of the shaded region, DEB, in the rectangle ABCD as shown in the diagram.

Triangle DCE is a right triangle with DE as the hypotenuse and DC = 3

Find EC using Pythagorean Theorem.

Area of shaded region is area of rectangle – (Area of )

**Solution**

**Q 3: Application**

The figure shows four right triangles with common vertex at and a side of unit length.

∆ABC is a right isosceles triangle with legs of unit length.

- Find the length of AC,AD,AE and AF
- How are the above sides related
- Find area of ∆ABC,∆ACD,∆ADE, and ∆AEF

**Solution**

The length of each hypotenuse is √n, n=2,3,4,5Note: This is how the ancient Greeks constructed accurate length of √n.

**Q4: Height of Pyramid**

The great Pyramid at Giza in Egypt has a square base with sides 220 m long. The distance from the top of the pyramid to each corner of the base is 233 m. Find the height of the pyramid.

**Solution :** Height of Pyramid

ABCD, the base of the pyramid is a square. Triangle ABC is right triangle.

Solve ∆ACB to find diagonal. Half of this diagonal helps to find the height while solving the ∆AOE.

Answer: Height of the pyramid is 173.5 m.

**Q5.** Find the longest diagonal length, AD, in the rectangular prism with dimensions of 3, 4, and 8 units. Round answer to 3 s.f.

**Solution :**

**Q6.** Find the height of the square based prism shown in the figure correct to 3 significant places.

**Solution :**

**Q7.** A wedge with square base is shown in the figure.

Find the length DC if the sides of the square are 1.2 m each and the height AB is 1.24 m.

**Solution :**

**Q8.** Find the distance of the chord AB from the center O of the circle with radius 10 cm if the chord length is 12 cm.

**Solution :**

Let OC be right bisector of AB

∆OCA is a right triangle since the right bisector of a chord will pass through the origin.